Mirroring the rally in Australian markets on Monday, Hong Kong's Hang Seng index jumped more than 10 per cent, while share prices in South Korea and Singapore were also higher.
But those in New Zealand fluctuated between positive and negative territories while stocks in China and Taiwan were down.
Japanese markets, which lost 24 per cent last week, were closed for a holiday on Monday.
Australia's move on Sunday to guarantee all its bank deposits came after the country's benchmark index lost 8.3 per cent on Friday - the worst one-day loss in 21 years.
Kevin Rudd, the Australian prime minister, also guaranteed the borrowings of Australian banks in international credit markets.
A scheme to purchase residential mortgage-backed securities was doubled to A$8bn, in an attempt to shore up the mortgage market.
The stock markets in Asia were the first on Monday to react to news that leaders of European countries using the euro had agreed on a plan to jointly confront the banking crisis by recapitalising banks and guaranteeing inter-bank lending.
Aela Callan, reporting for Al Jazeera from Hong Kong, said the rescue plan may have been welcome news to some investors, but some Asian economies have problems of their own.
Specifically, China, Taiwan and Hong Kong are all export-dependent economies and there are mounting fears that the sharp downturn in the US and Europe - the major buyers of those exports - will reduce exports, profits and jobs in the Asian countries.
On Sunday, Nicolas Sarkozy, the French president, anounced that leaders from the 15-member single currency Eurozone had reached an action plan to shore up the bloc's economy.
He said the countries would unveil the details of their national plans on Monday, but all had agreed on a specific series of measures designed to restore confidence in the economic system.
"This is indeed a joint action that we are undertaking. This plan addresses all aspects of the financial crisis," he said.
"The crisis has over the past days entered into a phase that makes it intolerable to opt for procrastination and a go-it-alone approach," he said.
Before joining his Eurozone colleagues, Sarkozy held bilateral talks with Gordon Brown, the British prime minister, to talk about his plans to partially nationalise some British banks.
Brown's appearance at the Paris summit came as The Sunday Times newspaper in London said Britain would launch its biggest retail bank rescue on Monday when the four largest banks - HBOS, Royal Bank of Scotland, Lloyds TSB and Barclays - ask for a combined $60.5bn lifeline.
The unprecedented move would make the government the biggest shareholder in at least two banks, HBOS and Royal Bank of Scotland, the newspaper said on its website.