This is CNBC's live blog covering European markets.

European stock markets closed lower on Tuesday as U.S. debt ceiling negotiations continued.

The region's benchmark Stoxx 600 index closed 0.6% lower, with sectors mixed as trading came to a close. Household goods fell 2.5% as industrials dropped 1.3%, while oil and gas stocks gained 0.9%.

The euro zone Composite Purchasing Managers' Index for May showed solid growth that continued to be driven by services, with manufacturing hit by weak demand and a fall in selling prices.

"Eurozone GDP is likely to have grown in the second quarter thanks to the healthy state of the services sector. However, the manufacturing sector is a powerful drag on the momentum of the economy as a whole," said Cyrus de la Rubia, chief economist at Hamburg Commercial Bank.

"German companies from this sector are particularly hard on the brakes, as new orders here have fallen even more significantly than in France and the production index is also pointing sharply downward."

On Monday, House Speaker Kevin McCarthy said he had a "productive" and "professional" meeting with President Joe Biden on how to raise the debt ceiling, but that the two did not reach a deal. June 1 is seen as the earliest date that the U.S. could default, lending urgency to the discussions.

Asia-Pacific markets closed mixed, while U.S. stocks were lower on debt ceiling concerns.

Climate protesters try to storm stage at oil giant’s annual shareholders meeting

Shell Chief Executive Wael Sawan and the firm's board of directors on Tuesday were shielded by security staff as climate protesters unsuccessfully tried to storm the stage at the British oil giant's annual shareholders meeting.

The acrimonious meeting, which was held at the ExCeL London exhibition center, was repeatedly disrupted by protesters before they were removed by security staff.

The full story is available here.

— Sam Meredith

There are signs that the services sector upturn is fading, economist says

Chris Williamson, chief business economist at S&P Global Market Intelligence, discusses the euro zone composite purchasing managers' index for May.

Expect bank valuations to be enhanced, says EBA chair

Jose Manuel Campa, chairperson for the European Banking Authority, discusses the banking turmoil and the prospect of consolidation in the industry.

U.S. stocks open lower

U.S. stocks fell Tuesday on the heels of a key debt ceiling meeting between President Joe Biden and House Speaker Kevin McCarthy that failed to produce a resolution.

The Dow Jones Industrial Average fell 124 points, or 0.4%. The S&P 500 dipped 0.4% along with the Nasdaq Composite

—CNBC's Christina Wilkie contributed to this report.

UK will avoid entering recession and have 'subdued' but positive growth, IMF says

The IMF estimates that the U.K. will avoid recession in 2023, but says the country's positive growth will be "subdued."

The latest release suggests the U.K. GDP will grow by 0.4% this year — a 0.7 percentage point increase on the financial agency's April estimate of a 0.3% downturn.

"Stubbornly high" inflation had served to hinder growth, the IMF said, along with the impacts of Russia's full-scale invasion of Ukraine and lingering supply scarring from the Covid-19 pandemic.

— Hannah Ward-Glenton

It’s ‘very naive’ to assume the Fed will cut interest rates this year, strategist says

Bob Parker, senior advisor at International Capital Markets Association, says that's despite the fact that the chance of the U.S. Federal Reserve raising interest rates further is "now very limited."

Euro zone PMIs down slightly in May

Euro zone business output maintained solid growth in May for a fifth straight month, though at a slower rate, according to S&P Global and Hamburg Commercial Bank's flash Composite Purchasing Managers' Index.

The survey showed a decline to 53.3 in May from 54.1 in April. A figure below 50 indicates a contraction.

It highlighted a "near-stalling of new business inflows" and widening divergence between the services sector, which is growing strongly, and manufacturing, where factory output is declining.

PMI figures also out Tuesday showed a similar disparity in Germany, where overall business output grew month on month but manufacturing experienced a downturn. In France, there was a "softening of demand conditions" that also hit services.

— Jenni Reid

Julius Baer down 8% after missing expectations

Swiss private bank Julius Baer fell 8.15% in early trade after its quarterly results missed expectations.

Assets under management edged up 1% to 429 billion Swiss francs ($476 billion) as it saw a slight rise in net money inflows, but took a hit from currency conversions as the franc strengthened against the dollar.

The bank said in a statement that the first quarter had been a "challenging backdrop for wealth managers" but that its "capital position and balance sheet liquidity were further reinforced from the already solid levels reported at the end of 2022."

— Jenni Reid

Europe stocks open lower

European stocks were lower in early Tuesday trade, with the Stoxx 600 index falling 0.34% after a directionless Monday.

Germany's DAX fell further still from the record high it hit Friday, down 0.13% on the previous session. France's CAC 40 dropped 0.4%, while the U.K.'s FTSE 100 was down 0.18%.

Travel saw the biggest fall by sector, down 0.7%.

— Jenni Reid

CNBC Pro: Asset manager reveals shorts position in these 4 global commercial property stocks

Shares of several global commercial property companies are set to decline further, according to chief investment officer Patrick Armstrong.

Armstrong, who manages equity strategy at wealth manager Plurimi, revealed that he is shorting four global commercial property companies.

"It's an expensive company, in my opinion, that's facing a pretty toxic environment," he said about one of his shorts.

CNBC Pro subscribers can read more here.

— Ganesh Rao

McCarthy and Biden meet as debt ceiling looms on markets

President Joe Biden and House Speaker Kevin McCarthy spoke to reporters around when they were scheduled to meet about the debt ceiling.

Biden said he was hopeful about progress and emphasized the need to ensure tax loopholes are closed so wealthy people pay a fair share of taxes. McCarthy said he was looking forward to finding common ground, after saying earlier in the day that decisions have to be made at the meeting.

Investors have been watching for updates on progress out of debt ceiling negotiations amid concerns for what a default could mean for the economy.

— Alex Harring

Yellen's latest guidance: 'Highly likely' Treasury will be unable to cover debts in early June

Treasury Secretary Janet Yellen has just released a new letter to congressional leaders with updated guidance on the earliest date that the U.S. could be at serious risk of a debt default.

The date remains June 1 in the new letter, the same date it's been since the start of May. But the new message contains two key differences from a very similar letter Yellen penned on May 15.

"With an additional week of information now available, I am writing to note that we estimate that it is highly likely that Treasury will no longer be able to satisfy all of the government's obligations if Congress has not acted to raise or suspend the debt limit by earlyJune, and potentially as early as June 1," writes Yellen.

The phrase "highly likely" is new. Last week Yellen wrote that it was merely "likely."

Yellen also removed an entire sentence from last week's letter that said emergency measures Treasury is currently taking could help to push that June deadline out.

"The actual date Treasury exhausts extraordinary measures could be a number of days or weeks later than these estimates," read Yellen's May 15 letter to congressional leaders.

The new letter comes as President Joe Biden is about to meet face to face with House Speaker Kevin McCarthy, part of an increasingly urgent effort to reach a bipartisan compromise deal.

— Christina Wilkie

CNBC Pro: Fund manager shares tips on investing sustainably — and generating big returns

Philip Ripman manages the $1 billion Storebrand Global Solutions fund, with a focus on sustainability. But as well as green energy stocks, he also invests in chipmakers, cybersecurity stocks, pharmaceuticals and more.

His strategy appears to have paid off over the long term: his fund ranks top for 10-year annualized returns (15%) on Morningstar's list of global mega-cap equity funds.

Here are three tips on investing sustainably, including how to play the renewables theme, according to Ripman.

CNBC Pro subscribers can read more here.

— Weizhen Tan

European markets: Here are the opening calls

European markets are expected to open higher Tuesday.

The U.K.'s FTSE 100 index is expected to open 12 points higher at 7,785, Germany's DAX 15 points higher at 16,241, France's CAC 8 points higher at 7,482 and Italy's FTSE MIB 34 points higher at 27,376, according to data from IG.

There are no major earnings releases. Data releases include preliminary purchasing managers' index figures for the euro zone in May. The data measures manufacturing and services activity in the bloc.

— Holly Ellyatt