The BBC's Business Editor Robert Peston said three types of credit guarantees would be offered, aimed at firms most in need and those of most significance to the economy.
Firstly, support for up to £10bn in short-term loans for medium-sized firms to help them meet their day-to-day financing needs.
Secondly, backing for loans to help financially sound but credit-starved companies with long-term investment, with specific support for exporters and companies with high-value jobs and products.
Thirdly, capital for strategically important small businesses which have overextended themselves during the credit boom.
Shadow chancellor George Osborne gives his view of the plans on Daily Politics
The BBC understands that the potential cost to the government of the guarantees, in terms of public spending and liabilities should loans not be repaid, will total several hundred million pounds.
The prime minister's spokesman said the government was considering options to ensure businesses and households get access to credit.
He added there would be "no irresponsible blanket guarantees" and that any measures would be "targeted, thought through and funded".
Lord Mandelson, who is expected to give a statement this week, said: "I want to make sure that, when we intervene, we intervene in a way that's really effective, really targets real, genuine business needs in a way that gives value for money from the government and the taxpayer's point of view, and is genuinely going to help businesses in what is a very difficult credit situation."
The Conservatives want a larger £50bn national loans guarantee scheme to get credit flowing again and help firms being affected by the unwillingness of banks to lend due to the impact of the credit crunch.
They say this would not expose the taxpayer to any risk, being effectively self-financing, but Labour claims that is totally unrealistic.
The dithering in government has cost the jobs of many people
Shadow chancellor George Osborne told the BBC: "The Conservative Party has been proposing the scheme now for more than two months.
"The dithering in government has cost the jobs of many people."
Liberal Democrat Treasury spokesman Vince Cable said: "The government should stop messing around with stunts and wheezes and ensure that the banks owned or part owned by taxpayers operate as state banks maintaining lending for the economy.
"The government has already invested £37bn of taxpayers' money recapitalising the banks. It has bottled out of ensuring that the banks comply with their undertaking to maintain lending to sound businesses.
"There can be no justification whatsoever for this huge sum of money being held back from good commercial borrowers."
Labour's credit proposals received a mixed response from business.
The CBI described the move as a good "first step" which would address the most chronic problem facing companies.
But entrepreneur and venture capital boss Jon Moulton said the proposed assistance was not nearly substantial enough.
He told MPs on the Treasury Select Committee that the £20bn was "not actually a very large number against the scale of the problems we are talking about".
"I would personally be happy if the scheme was a lot larger," he added. "We are in a bad hole and we need to get out of that hole."
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