WASHINGTON  The Obama administration put the nation’s biggest banks on notice Monday that the government could become their biggest shareholder if regulators decide they are not strong enough to weather a deeper-than-expected downturn in the economy.

In an unexpectedly assertive joint statement, the Treasury Department, Federal Reserve and federal bank regulatory agencies announced that the government might end up demanding a direct ownership stake in major banks after they undergo a tough evaluation of their strength, which is to begin shortly.

“The capital needs of major U.S. banking institutions will be evaluated under a more challenging economic environment,” the administration said. “Should that assessment indicate that an additional capital buffer is warranted,” it continued, the banks could be required to give the government a right to acquire common shares, with voting rights.

The statement came as federal regulators confirmed that they were in discussions with Citigroup over precisely that kind of swap. Citigroup, which has received $45 billion in direct assistance and given the Treasury nonvoting preferred shares that pay a guaranteed dividend  is negotiating to swap the preferred shares for common shares that would give the government a stake as high as 40 percent.