WASHINGTON — President-elect Barack Obama asked President George W. Bush today to seek another $350 billion to bail out the financial sector so that Obama can have the money at his disposal promptly after taking office.

Bush agreed to notify Congress, the White House said. Congress has 15 days to reject the request, but efforts were afoot to have the money available for Obama much sooner.

The request would give Obama not only the opportunity to get quick access to the money, but also to change the program’s goals and conditions. The Bush administration’s handling of the first $350 billion has come under widespread criticism in Congress and from watchdog organizations.

Obama and his economic team have signaled that he was eager to use the money to help reduce the number of mortgage foreclosures and that he wanted to place greater restrictions on institutions that receive the funds. The move comes as Democrats in the House of Representatives prepare to act on similar legislation.

Earlier today, Bush said he would not request the money from Congress unless Obama “specifically asked me to make it.” About two hours later, White House press secretary Dana Perino said that Obama had indeed asked Bush to submit the request.

Bush’s assertion that the decision to tap the money rests with Obama was an acknowledgment of what has been an extraordinary ceding of power to the incoming administration. In fact, when it comes to the economy, Bush in recent weeks has let Obama be the driving force behind most recovery efforts.

A vote in Congress is likely soon, possibly this week, several senators predicted after a briefing from Obama economic adviser Larry Summers on the Wall Street bailout, as well as on Obama’s separate plan for roughly $800 billion in spending and tax breaks to spur the economy.

“I feel better this morning, and I am told the Obama team will be giving us these specifics” on precisely how the additional money would be disbursed, said Senate Banking Committee Chairman Christopher Dodd, D-Conn., after talks with Summers.

Though Bush would request the additional money for the Troubled Asset Relief Program, the incoming Obama administration would sell the plan by laying out a series of changes in how the program is run.

Obama’s nominee for Treasury secretary, Timothy Geithner, has been working to redefine the program and to impose more conditions on how the money is used.

“Larry Summers made a very strong argument for why it’s important and critical for the overall recovery,” said Sen. John Kerry, D-Mass. “And I think that’s an argument that most senators understand.”

Summers sought to win over Senate Democrats even as the GOP leader of the House, John Boehner of Ohio, warned that any effort to release the additional money would be a tough sell.

At his news conference, Bush defended the financial industry bailout, a massive government intervention that has drawn criticism from Republicans as an intrusion into the financial markets and from Democrats who complain the money has not helped stabilize or reduce mortgage foreclosures.

“I readily concede I chucked aside some of my free market principles when I was told by chief economic advisers that the situation we were facing could be worse than the Great Depression,” Bush said.

He credited the program for improving the lending landscape.

“Credit spreads are beginning to shrink,” he said. “Lending is just beginning to pick up.”

Congress approved the program in October, authorizing $700 billion to assist the financial industry. The Bush administration has already committed the first $350 billion, using it to inject capital into banks and to bail out ailing major companies considered too big to fail without further damage to the economy. Money from the program has gone to insurance giant American International Group Inc. and automakers General Motors Corp. and Chrysler LLC.

Lawmakers from both parties have criticized the administration’s handling of the fund, in part because the financial institutions that have received the unconditional sums of money have done little to account for it.

Treasury Secretary Henry Paulson originally promised the money would be used to buy up toxic mortgage-related securities whose falling values have clogged credit markets and brought many financial institutions to the brink of failure.

A request to Congress would force a vote within days on whether to block the funding, but the deck is stacked in favor of Bush and Obama winning release of the remaining $350 billion. Congress can pass a resolution disapproving the request, but the White House could veto the resolution; then, just one-third of either chamber would be needed to uphold the veto and win release of the money.

“The (incoming) administration ... is going to fundamentally alter how this is being managed,” Dodd said. “The concept is still very sound and solid and it is needed. But it’s not going to pass around here unless there’s a strong commitment to foreclosure mitigation.”

“These assurances have to be forthcoming, if they’re not, we’re going to have trouble passing this,” he said Monday on CBS’s “The Early Show.”