European equities rebounded on Tuesday after fears over the possible collapse of Chinese property giant Evergrande sparked a rout across global markets in the prior session, but a mild rally on Wall Street petered out.

Markets on both sides of the Atlantic were battered on Monday by fears that Evergrande's troubles could spill into their financial systems, leading major indices to lose between one and two percent.

European sentiment was decisively positive on Tuesday, with London gaining one percent, Frankurt rising 1.2 percent and Paris adding 1.3 percent.

On Wall Street, the Dow and S&P 500 were periodically positive but slumped near the close to post slight losses. The Nasdaq scraped a meager 0.2 percent gain.

The picture was mixed in Asia, with Hong Kong closing up 0.5 percent but Tokyo slumping 2.2 percent, while Shanghai was closed for a Chinese public holiday.

In Asia trading, Hong Kong-listed real estate firms, which took the brunt of the selling on Monday and tanked more than 10 percent, eked out gains.

There were indications the Evergrande crisis was improving. Founder Xu Jiayin said in a letter to staff that he "firmly believes Evergrande will be able to step out of the darkest moment soon."

But the real estate developer, which has fallen more than 80 percent this year alone, ended further in negative territory.

Attention is on what happens next in the Evergrande saga, with the firm -- wallowing in debts of more than $300 billion -- due to pay interest to bondholders on two notes on Thursday.

Beyond the Chinese saga, "worries about stretched valuations, peak policy support and political gamesmanship between -- and within -- the parties in Washington have kept the market's bullish bias in check," wrote Briefing.com analysts.

Observers predict the US Federal Reserve will use its policy meeting beginning on Tuesday to set out its timetable for tapering the vast bond-buying monetary easing program that has been a key driver of a global recovery for more than a year.

A battle in Washington to raise the US debt limit was, however, fueling concern the government could miss payments on its debt obligations and spark a disastrous default.

Rising Covid-19 infections, a slowing global recovery and a brewing energy crunch are also weighing on markets.

The International Energy Agency urged Russia to send more gas to Europe, as the continent faces skyrocketing prices for fuel.

The OECD on Tuesday warned of an "uneven" global economic recovery, as it lowered its 2021 growth forecasts for the world and the United States, while raising the outlook for Europe.

On the corporate front, shares in Universal Music, the world's biggest label with a lineup of megastars from The Beatles to Taylor Swift, surged on its stock market debut, giving the company a valuation exceeding $50 billion.

Investors -- already battling concerns about Evergrande, the virus and Fed monetary tightening -- are keeping a nervous eye on Capitol Hill as US lawmakers struggle to lift the country's debt ceiling in order to pay its bills
Investors -- already battling concerns about Evergrande, the virus and Fed monetary tightening -- are keeping a nervous eye on Capitol Hill as US lawmakers struggle to lift the country's debt ceiling in order to pay its bills AFP / Samuel Corum

New York - Dow: DOWN 0.2 percent at 33,919.84 (close)

New York - S&P 500: DOWN 0.1 percent at 4,354.19 (close)

New York - Nasdaq: UP 0.2 percent at 14,746.39 (close)

London - FTSE 100: UP 1.0 percent at 6,970.24 (close)

Frankfurt - DAX: UP 1.2 percent at 15,313.05 (close)

Paris - CAC 40: UP 1.3 percent at 6,539.52 (close)

EURO STOXX 50: UP 1.3 percent at 4,097.51 (close)

Hong Kong - Hang Seng Index: UP 0.5 percent at 24,221.54 (close)

Tokyo - Nikkei 225: DOWN 2.2 percent at 29,839.71 (close)

Shanghai - Composite: Closed for a holiday

Euro/dollar: DOWN at $1.1724 from $1.1726 at 2100 GMT

Pound/dollar: UP at $1.3659 from $1.3657

Euro/pound: DOWN at 85.82 pence from 85.86 pence

Dollar/yen: DOWN at 109.21 yen from 109.44 yen

Brent North Sea crude: UP 1.0 percent at $74.68 per barrel

West Texas Intermediate: UP 0.3 percent at $70.51 per barrel