Monday's session started on a negative note, with markets suffering hefty falls but the losses were reduced after the US and Russian leaders said they would hold talks on Ukraine, as long as Putin does not invade.
The US is "committed to pursuing diplomacy until the moment an invasion begins", Biden's press secretary Jen Psaki said in a statement. "President Biden accepted in principle a meeting with President Putin ... if an invasion hasn't happened."
"We are also ready to impose swift and severe consequences should Russia instead choose war. And currently, Russia appears to be continuing preparations for a full-scale assault on Ukraine very soon."
The news raised hopes for a peaceful conclusion to the standoff, though traders remain on edge.
Tokyo, Hong Kong, Shanghai, Seoul, Singapore, Taipei, Manila and Wellington were in the red, though Sydney and Jakarta edged up slightly.
Gold, a safe-haven asset in times of turmoil, slipped.
Oil was also down on easing fears about the possibility of supplies being hit by any conflict in eastern Europe, though surging demand as the global economy reopens continues to put upward pressure on the commodity.
Observers are warning $100 will soon be breached and could hold above that level for an extended period, even if talks on Iran's nuclear programme succeed and lead to the resumption of Tehran's crude exports.
The sharp rise in crude is a key driver of inflation across the planet, adding to supply chain snarls and bottlenecks.
While expectations are for a Fed rate hike next month, some bank officials at the weekend indicated they were not in favour of a 50 basis point rise, as has been suggested in light of consumer price hikes.
The prospect of higher borrowing costs this year has weighed on markets for months, bringing a near two-year equity rally to an end with commentators predicting further volatility down the line.
"Global data and central banks' stance on tightening are all taking a backseat to Ukraine, with markets nervously awaiting the next headline," Su-Lin Ong, at Royal Bank of Canada, said. "Thinner liquidity because of the US holiday adds to the anxiety."