However, he cautioned that the US economy remained under "severe stress" and said there was still "a lot of work" to do.
Officials in attendance
Among those attending the White House meeting were Timothy Geithner, the US treasury secretary, and Ben Bernanke, chairman of the Federal Reserve.
Lawrence Summers, senior economic adviser to Obama, and Sheila Bair, head of the US Federal Deposit Insurance Corporation, were also present.
Obama was also briefed on the "stress tests" being conducted on around 20 of the nation's biggest banks, whereby the banks are being examined to see how they would fare in adverse economic conditions.
The results of the tests, due at the end of April, are highly anticipated by global markets anxious to see which firms are considered healthy and which firms may need more government assistance.
Robert Gibbs, the White House press secretary, said on Thursday he was unaware of any White House plans to reveal the results, but said the administration felt it was "important that there be some transparency around [the issue]."
Once the stress tests are finished and the banks' needs are determined, banks will have six months to raise capital in the private market or they could also receive government funds.
The government would also use public-private investment funds to soak up banks' toxic assets to help those financial institutions in need.
US government sources told Reuters that regulators would also discuss with Obama what steps may be necessary after the tests, but said officials would not necessarily close any banks based on the results.
The White House talks took place as some financial analysts said the US economy, currently in recession, is showing signs of possible turnaround.
They point to strong profit forecasts from banking giant Wells Fargo, a drop in unemployment benefit filings last week and a shrinking of the US trade deficit.
Summers said on Thursday there had been "substantial anecdotal flow" over the last six to eight weeks indicating that the US economy "felt a little bit better".
"The sense of a ball falling off a table, which is what the economy has felt like since the middle of last fall," he said.
"I think we can be reasonably confident that that is going to end within the next few months, and we will no longer have that sense of a free fall."