Senior finance officials met political leaders in Washington
US officials are working on a plan to help rid US banks of their bad debts in order to tackle the devastating global financial crisis.
After a meeting with Congress members late on Thursday, US Treasury Secretary Henry Paulson said new laws were needed to deal with the "root" of the problem.
It comes after a series of seismic shocks in the world's financial system.
The news boosted European and Asian shares. On Thursday, US shares added 3.9% after the plan was leaked.
Japan's Nikkei jumped 3.8%, while the Shanghai Composite recovered from 22-month lows to close up 9.5% and Hong Kong's Hang Seng soared 8.3%.
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US stocks had surged on Thursday because of reports of the rescue plan, with the Dow Jones Industrial Average ending 3.9% up at 11,019.69.
The proposed US government rescue plan comes at the end of a week of almost unprecedented turmoil on world financial markets amid a crisis of confidence in banks:
* US Wall Street giants Morgan Stanley and Goldman Sachs are the latest to have their shares punished by nervous investors amid concerns for their financial health
* Central banks around the world have pumped billions of dollars of extra funding into money markets to ease the liquidity crisis
* The UK's City watchdog announced a crackdown on short selling - thought to be a big contributor to the share price falls in UK banks in recent days.
* The US financial regulator the Securities and Exchange Commission followed suit on Friday, temporarily banning short selling in the stock of financial companies
* Stock markets in Russia were closed for a third day shortly after reopening on Friday amid concerns that shares rebounded too sharply after sharp falls earlier in the week
'Best of the US'
Mr Paulson and Federal Reserve Chairman Ben Bernanke briefed Congress leaders on the measures they were considering.
This country is able to come together and do things quickly when it needs to be done for the good of the American people
Henry Paulson,
Treasury Secretary
US public fears 'troubling times'
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"We talked about a comprehensive approach that will require legislation to deal with illiquid assets on financial institutions' balance sheets," Mr Paulson said.
He said the root cause of the stress in the markets was the "price declines in real estate".
In an upbeat press conference, the congressional leaders and financial regulators were keen to stress they had agreed to work together for the good of the country.
"I think we saw the best of the United States of America in the Speaker's office tonight," Mr Paulson said.
"This country is able to come together and do things quickly when it needs to be done for the good of the American people."
Some analysts gave a positive reaction to the news of a possible bail-out plan.
"It's a relief, it allows for an orderly workout for the impaired assets and it will help the banking sector get back to business," said Hans Kunnen of Colonial First State Fund Managers in Australia.
Central bank action
There is speculation that one plan being discussed involves legislation that would force lenders to renegotiate mortgages that homeowners are having difficulty paying.
Wall Street traders
Markets have been jittery amid huge upheavals in the banking sector
Another possibility is establishing a government agency that would take on the debt.
Reports said Mr Paulson was looking into setting up something akin to the Resolution Trust Corp (RTC), which was formed after savings and loans banks collapsed in the 1980s.
The RTC took over most of the smaller banks in the US at a cost of $400bn - about $1 trillion (£550bn) in today's money - and then tried to sell off their assets.
The cost of such a bailout would probably be higher this time, with bad mortgage debt believed to be around $2 trillion.
But Congressman Barney Frank, chairman of the House Financial Services Committee, said the plan would probably not involve creating a new government agency.
"There is this concern that if you had to wait to set up an entity, it could take too long."
Six of the world's top central banks took steps to calm worried stock markets on Thursday, releasing $180bn to lift the amount of credit available.
On Friday, the Bank of Japan said it had injected a further two trillion yen ($19bn; £10.5bn) into money markets, to add to the eight trillion yen it had already made available this week.