Investors pointed to the broadly positive market backdrop with central bank money-printing and the recovery in the world economy post-pandemic as reasons to stay bullish.
"Accommodative monetary and fiscal policies and macro recovery are still suggesting a buy-the-dip strategy," said Angelo Meda, head of equities at Banor SIM in Milan.
But some caution lingered, given simmering worries about the spillover from an Evergrande debt default, as well as a raft of central bank meetings including Wednesday's Federal Reserve statement that may bring the bank a step closer to tapering.
MSCI's index of world stocks edged up 0.14%, having plunged 1.6% on Monday. S&P 500 futures were almost 1% higher but the index stands around 4% below record highs hit in early-September
Asian shares sold off earlier on Tuesday with Hong Kong's Hang Seng .HSI down 0.1% by late afternoon, while Japan's Nikkei returned from a market holiday with a drop of 2%.
China's yuan steadied in offshore trade, recouping some of the losses that sent it to a three-week low on Monday. Evergrande shares fell 0.4% as focus now shifts to Thursday when the company is due to make bond interest payments.
An all-staff letter from chairman Hui Ka Yuan promised the firm would fulfil its responsibilities and "walk out of its darkest moment".
Struggling for cash, the developer owes $305 billion and markets worry a messy failure could reverberate through China's property sector and everything exposed to it - primarily banks and then the broader economy.
While Chinese mainland markets are closed for a public holiday, there was little evidence of that yet. Major Chinese state media made no mention of Evergrande's troubles, and Beijing has showed no sign of intervening.
Australian stocks rose 0.35% as miners BHP and Rio Tinto attempted to bounce back from nine-month troughs hit on Monday amid demand fears.
Copper hovered near one-month lows however, due to fears about demand for the metal widely used in construction.
Cryptocurrencies too found a floor, with bitcoin bouncing off 1-1/2-month lows.
Evergrande aside, other market tests loom, with central banks spanning the United States, Britain, Japan, Norway, South Africa, Sweden and Switzerland meeting this week.
Nerves ahead of the Fed kept the dollar from moving much lower, though it notched small losses against the euro and the Aussie, with the euro at $1.1735.
Ten-year U.S. Treasury yields crept up to 1.3277% even if many analysts now reckon details of the Fed's taper timeline may not be announced until November.
"Central banks rightly need to think about the ways they withdraw from these historically high levels of monetary accommodation, but the task is being made much more difficult by Evergrande and by fiscal blockages in the U.S," GSFM investment strategist Stephen Miller said.
He was referring to Congressional wrangling over passing a spending package and lifting the Treasury's borrowing limit.
The OECD said it was too early for governments and central banks to withdraw exceptional support for their economies.
Central banks will likely be watching gas price moves, with sharp price increases possibly exacerbating inflation risks and hurting the economic recovery. European gas prices, up some 280% this year, slipped a touch after an 11% jump on Monday.
Brent crude prices meanwhile rose by more than 1%, ending days of losses sparked by the Chinese property developer's troubles.
(Additional reporting by Tom Westbrook in Singapore, Hideyuki Sano in Tokyo, Anushka Trivedi in Bengaluru, Paulina Duran in Sydney, Danilo Masoni in Milan; Editing by David Evans and Edmund Blair) ((firstname.lastname@example.org ; +44 207 542 6176/020 7536 7473/44 7990567646))