Aljazeera's Cath Turner, reporting from Washington, said: "It's a significant shift in thinking by Bernanke - in July he said it was too early to consider another package.
"This time though, Bernanke suggested some of the stimulus should be directed at the credit markets - making credit more available to consumers, homeowners and businesses."
Asked by reporters whether the US was now in a recession, Bernanke said there was "a serious slowdown in the US ... whether it's called a recession or not is of no consequence".
Turner said Bernanke had been "very careful to avoid using the word "recession" as he would aware of the potential disastrous affects on markets if he was to further dent investors' confidence.
In a White House statement, George Bush, the US president, said he was "open" to the idea of a second economic stimulus plan.
Henry Paulson, the US treasury secretary, announced that nine major US banks had taken up a government offer to buy shares in their corporations.
"Our purpose is to increase confidence in our banks and increase the confidence of banks so that they will deploy - not hoard - their capital," he said.
"And we expect them to do so, as increased confidence will lead to increased lending."
A total of $250bn has been set aside for the programme - part of the $700bn rescue package that was signed off by congress - and several other banks are also expected to apply.
The Dow Jones index of leading US shares closed 4.7 percent, or 413 points, higher at 9,265 following what traders said was an increased confidence among investors who saw an easing of credit markets as a sign the government's attempts to aid the economy were working.
London's FTSE 100 earlier closed 5.41 per cent higher at 4,282.67 points. Shares on Paris' CAC index ended up by 3.56 per cent and Frankfurt's Dax closed 1.12 per cent higher.
The increases came after Sweden unveiled a plan to support banks with $200bn in credit guarantees in a move to improve liquidity and also said it would also create a $2bn "stability fund" to bail out any Swedish banks that run into solvency problems.
Japan's benchmark Nikkei 225 index rose by nearly 3.5 per cent in early trading on Tuesday to reach 9,319 points.