This is CNBC's live blog covering European markets.

European stocks closed higher Tuesday, with global markets lacking clear direction ahead of the new round of central bank interest rate decisions.

The pan-European Stoxx 600 index bounced either side of the flatline in morning trade and closed 0.4% higher, clawing back most of Monday's losses.

Sectors traded across positive and negative territory, with gains led by a 1.2% uptick in healthcare stocks. Oil and gas stocks were down 0.3% as global growth concerns counteracted the weekend's announcement of Saudi output cuts.

European Central Bank President Christine Lagarde said Monday there were "signs of moderation" in core inflation in the euro zone, but emphasized that it was too early to call a peak. The latest data showed inflation easing more than expected for May to 6.1%, but that figure remains well above the 2% target.

Asia-Pacific markets traded mixed Tuesday, while U.S. stocks were slightly higher.

Europe stocks close higher

Europe stocks closed higher Tuesday, with the Stoxx 600 up 0.4%.

The U.K.'s FTSE 100 ended 0.37% higher, with Germany's DAX up 0.18% and France's CAC 40 up 0.11%.

— Jenni Reid

U.S. stocks fall in early trading

The Dow slid about 50 points, or 0.2%. The S&P 500 pulled back 0.2% and the Nasdaq fell 0.4%.

— Fred Imbert

Oxford Metrics discusses its role in Abba Voyage and developments in VR

Nick Bolton, CEO of Oxford Metrics, the company behind the Abba Voyage holograms, discusses its earnings and the growth in augmented and virtual reality.

Euro zone consumers feel more positive about inflation, ECB survey shows

People living in the euro zone are feeling more upbeat about inflation, according to a survey conducted by the European Central Bank.

Findings show that consumer inflation projections have dropped significantly, with median expectations for inflation over the next 12-month period decreasing to 4.1% in April, from 5% in March.

The majority of respondents also anticipated lower growth in their house prices over the next year, along with declines in mortgage interest rates.

— Hannah Ward-Glenton

Fintech firm Nium plans U.S. IPO in 2 years, CEO says

Prajit Nanu, co-founder and CEO at Nium, says the company will be profitable in the next three to four quarters as it looks toward going public.

Klaas Knot: Inflation is stubborn but ECB policy is starting to work

Euro zone core inflation is proving sticky, but actions taken by the European Central Bank are starting to pay off, according to Klaas Knot, president of the Dutch central bank.

The ECB has hiked rates a total of 375 basis points in the past year in an attempt to tackle soaring inflation, and money markets are believed to have priced in another two 25-basis-point rate increases for the coming meetings, Reuters reported.

— Hannah Ward-Glenton

Germany manufacturing drops unexpectedly in April

Manufacturing orders in Germany fell by 0.4% in April, according to the Federal Statistical Office. Analysts polled by Reuters had forecast a 3% increase. New industrial orders were down 9.9% compared to the same month in 2022.

The manufacturing of machinery and equipment and miscellaneous vehicle construction were noticeable drags on the new order figure.

— Hannah Ward-Glenton

CNBC Pro: Here's what to buy — and avoid — after the U.S. debt ceiling deal, according to analysts

There are opportunities for investors — but also potential minefields — when the debt ceiling is lifted, such as an influx of Treasurys, according to some analysts.

In a June 4 report, Citi said it expects a net increase of about $400 billion in U.S. Treasury bill issuance in the near term — the bulk of it in short-duration bills.

Here's how analysts recommend trading the debt ceiling aftermath.

— Weizhen Tan

CNBC Pro: Ark Invest's flagship fund sold Nvidia before its big rally. Here's why

Tech giant Nvidia has been the darling of Wall Street this year due to a relentless rally in its stock driven by surging demand for artificial intelligence.

However, Ark Invest's flagship Ark Innovation ETF exited Nvidia entirely in early January before the chipmaker enjoyed a powerful rally that propelled it to a $1 trillion market capitalization.

Frank Downing, a research director at Ark Invest, spoke to CNBC about the investment house's decision to exit its Nvidia position from its flagship fund.

CNBC Pro subscribers can read more here.

— Ganesh Rao

European markets: Here are the opening calls

European markets are expected to open mixed Tuesday.

The U.K.'s FTSE 100 index is expected to open 8 points lower at 7,591, Germany's DAX 15 points lower at 15,947, France's CAC flat at 7,196 and Italy's FTSE MIB 21 points higher at 26,848, according to data from IG.

Data releases include euro zone retail sales for April. There are no major earnings releases.

— Holly Ellyatt