This was CNBC's live blog covering European markets.

European stocks shifted lower Tuesday as major markets returned to action after the Easter weekend and investors looked ahead to the start of a new trading quarter.

The pan-European Stoxx 600 index provisionally closed 0.76% lower, down sharply from earlier in the session. The majority of sectors were trading in the red, with retail stocks down 2.1%, although mining stocks rose 1.9%.

U.S. stocks were also lower Tuesday, after the S&P 500 and the Dow Jones Industrial Average kicked off April with declines.

European markets closed the first quarter of 2024 around 6.8% higher Thursday as recent inflation data continues to show that pressures from higher prices are cooling.

On Tuesday, investors digested fresh data for March on euro zone manufacturing, German inflation and U.K. house prices.

In Asia-Pacific markets, Hong Kong stocks led gains as Xiaomi shares surged, while investors assessed economic data from South Korea and Australia.

Europe markets close lower

European equity markets closed in the red on Tuesday, the first trading day of the new quarter.

Germany's DAX dropped 1.1%, while France's CAC 40 fell 0.9% and the U.K.'s FTSE 100 dipped 0.2%.

— Jenni Reid

Commodity prices pushed to highest levels since August 2022

Surging oil prices have pushed a broad-based commodity index to its highest level since the summer of 2022.

As the price of U.S. crude has jumped more than 18% in 2024, the CRB Commodity Index has risen nearly 11%. The index on Monday closed at its highest level since Aug. 30, 2022.

The CRB measure is comprised of 19 different raw materials including energy, agricultural products, precious metals and industrial metals. Other significant contributors to its increase this year include gold, up nearly 8%; sugar, up about 12% and copper, a traditional economic barometer that has risen 4.5%.

—Jeff Cox

U.S. stocks open in the red on Tuesday

The S&P 500 opened 0.9% lower, while the Dow Jones Industrial Average lost 340 points, or nearly 0.9% shortly after 9:30 a.m.. The Nasdaq Composite, meanwhile, slid 1.2%.

— Pia Singh

German inflation falls in six key states

Germany saw inflation fall in six key states last month, preliminary data showed Tuesday, in another boost for the fight against inflation.

Inflation in the various economically significant regions fell to 3.5% or below in March, compared to February, according to Reuters.

Euro zone inflation data due Wednesday will provide more indication on the path of price rises ahead of the European Central Bank's next interest rate decision in April.

— Karen Gilchrist

Euro zone inflation figures point to ECB rate cut in June, economist says

The latest euro zone inflation figures support the growing consensus that the European Central Bank will begin cutting interest rates in June, according to Chris Williamson, chief business economist at S&P Global Market Intelligence.

The ECB is "very data-dependent, and we're seeing signs of inflation really starting to come down now," Williamson told CNBC's "Street Signs Europe," calling June the "most realistic" month for rate cuts to start.

Headline consumer price inflation in France, Spain and Italy came in lower than expected last week, and on Tuesday, closely watched state-level inflation in Germany showed a decline in six key regions. A survey from Germany's Ifo Institute meanwhile showed company price expectations at the lowest level in three years.

"Those headline inflation numbers coming down are going to give the ECB not just some comfort that current inflation is down, but also that you're going to see reduced wage negotiations, as lower inflation means workers have less grounds to negotiate higher pay. So it forms this nice virtuous cycle of lower inflation, so that's really what we've been waiting to see," Williamson said.

There have also been signs of easing cost pressures in the services sector, a main area of concern for the ECB, which has "added to the case" for rates starting to come down in June, Williamson said.

— Jenni Reid

Stocks on the move: SSAB falls 4.5%, Delivery Hero up 6%

Shares of Swedish steelmaker SSAB fell 4.5% in early deals after it announced that it will invest 4.5 billion euros ($4.83 billion) in building a fossil-free mini-mill in the country.

On the other end, Delivery Hero rose 6% following reports that Singapore's competition watchdog had launched a probe into its now abandoned takeover of Southeast Asia delivery business Grab. Shares of Just Eat were also up 4.4%.

— Karen Gilchrist

Euro zone factory activity falls further in March

Euro zone manufacturing activity took a deeper dive in March, contracting at a greater pace than the previous month, new data showed Tuesday.

The HCOB's euro zone manufacturing purchasing managers' index fell to 46.1 in March from February's 46.5.

It marks the 21st month that activity has been below the 50 mark.

— Karen Gilchrist

UK house prices mark fastest rise since December 2022

U.K. house prices increased 1.6% in March from a year earlier, marking the fastest rise since December 2022, new data from British mortgage lender Nationwide showed.

Prices dropped 0.2% in March alone, the first drop since December 2023 after a 0.7% increase in February.

"Activity has picked up from the weak levels prevailing towards the end of 2023 but remain relatively subdued by historic standards," said Robert Gardner, chief economist at Nationwide.

"This largely reflects the impact of higher interest rates on affordability. While mortgage rates are below the peaks seen in mid-2023, they remain well above the lows prevailing in the wake of the pandemic," he added.

— Karen Gilchrist

CNBC Pro: 'Very, very attractive': Strategist names two under-the-radar U.S. small cap names to play right now

Market strategist Matt Orton sees promise in small mid cap stocks this year, naming four under-the-radar companies he is bullish on right now.

"I have been optimistic around small-caps this year, and it looks like we could be on the verge of an even bigger breakout," Orton, who is the chief market strategist at asset management firm Raymond James Investment Management told CNBC's "Squawk Box Asia" on April 1.

Small cap players in the U.S. stand out to him as "very, very attractive" right now, he said, naming two under-the-radar companies he likes.

CNBC Pro subscribers can read more here.

— Amala Balakrishner

CNBC Pro: Five stocks to buy and hold for the long-term, according to the pros

Investing for the long-term is no mean feat.

A longer investment period involves "looking for business models and strategies that are likely to stay for say 10, 20 or even 40 years from now," says David Dietze, managing partner and senior portfolio strategist at Peapack Private Wealth Management.

CNBC Pro spoke to three fund managers on their stocks to to buy now and hold for the longer-term.

CNBC Pro subscribers can read on their top five stocks picks here.

— Amala Balakrishner

European markets: Here are the opening calls

European markets are set to open mixed Tuesday.

The U.K.'s FTSE 100 index is expected to open 5 points lower at 7,957, Germany's DAX up 10 points at 18,516, France's CAC 14 points higher at 8,222 and Italy's FTSE MIB down 91 points at 34,209, according to data from IG. 

U.K. house price data, euro zone manufacturing numbers and German inflation figures for March are all due.

— Karen Gilchrist