(Corrects spelling of last name of Securities and Exchange Commission chair to Schapiro from Shapiro)

By Matt Spetalnick

WASHINGTON, April 10 (Reuters) – President Barack Obama said on Friday the recession-hit U.S. economy was showing “glimmers of hope” despite remaining under strain and promised further steps in coming weeks to tackle the financial crisis.

“We’ve still got a lot of work to do,” Obama told reporters after a meeting with economic and regulatory teams plus Federal Reserve Board Chairman Ben Bernanke. But he added, “We’re starting to see progress.”

Obama spoke a day after encouraging trade and jobless figures pushed stocks higher, and White House economic adviser Lawrence Summers predicted the economy would emerge from a sense of “freefall” by the middle of the year.

Less than three months into his presidency, Obama stopped short of declaring that the recession he inherited from predecessor George W. Bush was bottoming out.

But he offered a somewhat more upbeat tone than he has recently on the state of the economy, which is locked in its worst crisis in decades. “What we’re starting to see is glimmers of hope across the economy,” he said.

“Over the next several weeks, you’ll be seeing additional actions by the administration,” he added but gave no details.

Obama made no mention of “stress tests” being conducted at 19 major U.S. banks. The results, due at the end of April, are anxiously awaited by the financial markets.

The White House had said Obama was to receive a status report on those appraisals on Friday. Attempting to assess banks’ capital needs, the government is testing how they would fare under more adverse economic conditions than are expected.

MARKET SENSITIVITY

Mindful of market sensitivity, the Treasury Department is asking banks not to talk about the stress tests as part of their first-quarter earnings results, according to a source familiar with government discussions.

Asked whether banks were being told to be silent, Obama adviser Austan Goolsbee told Fox Business Network: “You ought to wait until the proper announcement time of all the bank examinations together, rather than have individual banks come running forward revealing their individual information alone.”

Obama did say, however, that he and his advisers discussed a program to use public-private sector investment funds to help banks clear their books of toxic assets.

He also voiced confidence that his administration was addressing problems in both the troubled banking system as well as non-bank financial institutions, a sector that escaped adequate regulatory scrutiny before the latest crisis.

Obama was briefed by Bernanke, Summers, Treasury Secretary Timothy Geithner, Federal Deposit Insurance Corp Chairman Sheila Bair, Securities and Exchange Commission chair Mary Schapiro and U.S. Comptroller of the Currency John Dugan.

Obama cited improvement in small business financing and what he called a “very significant” pickup in mortgage refinancing needed to stabilize the troubled housing market.

But he added, “The economy is still under severe stress.”

(Editing by Sandra Maler)