Asian markets were mixed Monday as US President Donald Trump signed a massive coronavirus relief bill, with a boost in positive sentiment dampened by concern over a new strain of COVID-19.

Under pressure from all sides, Trump approved the stimulus package worth $900 billion late Sunday in the United States, having delayed doing so for nearly a week.

"An otherwise quiet day in Asia has sparked to life," Jeffrey Halley, Senior Market Analyst at OANDA, said after the signing.

"The headline should provide a welcome boost to sentiment in Asia, which was likely to waver today as Chinese authorities over the weekend told Ant Financial to go back to its core payments business," he added.

Before signing the bill, Trump tweeted that he had "good news" to come, sending markets swinging higher even before the measures were approved.

Equities and oil prices have taken a hit recently as virus cases surged across the planet and a new more transmissible strain was reported in Britain, forcing governments to impose tight restrictions and lockdowns to contain the disease over the festive period.

Tokyo closed 0.7 percent higher on Monday, with Jakarta, Mumbai and Bangkok also in positive territory.

Shanghai, Seoul and Singapore were flat, while Hong Kong closed down 0.3 percent and Manila slid 1.1 percent.

Sydney and Wellington were closed for a holiday.

European stock markets opened firmer. Paris was up 0.7 percent and Frankfurt rose 1.3 percent, with dealers citing the Brexit trade deal as a major positive for Europe's biggest economy and trade powerhouse. London was closed for a holiday.

The emergency US package is part of a larger spending bill that, with Trump's signature, will avoid a government shutdown on Tuesday.

The president's turnaround came after a day marked by calls from across the political spectrum for action to avert a financial and social disaster in the world's largest economy, especially among the most vulnerable.

"For Americans that have been endlessly checking their mailboxes for a stimulus check, this is the best holiday present anyone could ask for," said Axi strategist Stephen Innes.

"The stimulus balloon will allow the markets to navigate better the number of new air pockets... due to the virus's latest variant," he added.

But with various lockdown measures in place worldwide due to the new strain, "vaccine rollout remains the key to unlocking the ultimate rally door", Innes warned.

The approval and roll-out of vaccines has boosted hopes that 2021 could bring a respite from the pandemic, which has killed more than 1.7 million people since emerging in China late last year.

But jitters remain over the new strain that emerged in Britain and reached several other European countries as well as South Korea and Japan.

Analysts in Tokyo said investors remained cautious after Japan reported its first cases of the new strain and closed its borders to all non-resident foreign arrivals until late January.

Over the weekend China's central bank summoned executives from Ant Group and demanded the fintech giant "strictly rectify" its lending, insurance and wealth management services, as the state squeeze continues on the once unbridled empire of tech tycoon Jack Ma.

Tokyo - Nikkei 225: UP 0.7 percent at 26,854.03 (close)

Hong Kong - Hang Seng: DOWN 0.3 percent at 26,314.63 (close)

Shanghai - Composite: FLAT at 3,397.29 (close)

Pound/dollar: UP at 1.3564 from $1.3533 late Friday

Euro/pound: UP at 90.02 from 89.98 pence

Euro/dollar: UP at 1.2224 from $1.2179

Dollar/yen: DOWN at 103.43 from 103.70 yen

West Texas Intermediate: DOWN 0.1 percent at $48.20 per barrel

Brent North Sea crude: DOWN 0.2 percent at $51.19 per barrel

New York - Dow: UP 0.2 percent at 30,199.87 (close)

London - FTSE 100: UP 0.1 percent at 6,502.11 (close)