The person, speaking on condition of anonymity, said if institutions are found to need additional capital, financial authorities will provide them with an "extra cushion of support."
Banks are expected to receive additional information about the tests in the coming week from regulators.
The largest U.S. banks are "well capitalized" for current conditions, the source said, but the Obama administration wants to ensure that they can withstand a more severe economic climate and can play an important role in maintaining the flow of credit.
Initial plans for the stress tests were announced Feb. 10 as part of Treasury Secretary Timothy Geithner's bank stabilization plan, but the source Saturday for the first time linked the tests to additional government support for large banks. This person did not specify what form any extra capital cushion may take.
Little is known about the form of the stress tests, but the person described them as "consistent, forward looking and conservative."
The Obama administration on Friday tried to ease market fears that the government was poised to nationalize some large banks that are continuing to struggle with losses and a lack of confidence, notably Citigroup and Bank of America.
Bank shares fell sharply, with Citigroup's (C, Fortune 500) plunging 22 percent to below the $2 price of a typical automated teller machine (ATM) fee and Bank of America (BAC, Fortune 500) trading around the $4 level.
White House spokesman Robert Gibbs said Friday that "this administration continues to strongly believe that a privately held banking system is the correct way to go."
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