The country's government said it would also create a $2bn "stability fund" to bail out any Swedish banks that run into solvency problems.
Earlier, Asian stocks were higher after South Korea was also forced prop up its banking sector.
The government had pledged $130bn in state guarantees and capital injections over the weekend.
However, some analysts said the steps were unlikely to be strong enough to reverse a fierce downtrend and that South Korea remained particularly vulnerable to the global credit squeeze.
Japan's benchmark Nikkei 225 index rose 311.77 points, or 3.59 per cent, to 9,005.59, climbing above the 9,000-level for the first time since Wednesday.
Chinese shares as lower third quarter inflation data and pledges of fresh government support for the economy buoyed buying sentiment.
Developers, financial stocks and miners lead the advance. Shares in India and Singapore also advanced during the day.
But investors remained cautious, many sticking to safer government bonds rather than buying riskier stocks after last week's rollercoaster ride, which saw global indices alternate between record lows and staging strong rallies.
Over the weekend, George Bush, the US president, announced he would host the first in a proposed series of global summits on the financial crisis, soon after the November 4 US presidential election.
The summits will focus on the "principles of reform" needed to fix the world's financial system, "so we can ensure that this crisis does not happen again", Bush said.
Kengo Suzuki, a currency strategist at Shinko Securities in Tokyo, told the Reuters news agency that the "slew of recent policy actions worldwide has provided some relief to the banking sectors in the major economies".
But dealers said that while stocks were much cheaper than just a few weeks ago, investors remained worried about the impact of the financial crisis on economic growth and corporate earnings.
"The state of the market remains very fragile with worries mounting about the global economy and emerging markets," Suzuki said.