The Congressional Black Caucus yesterday warned President Carter that it intnds to try to mobilize public opinion in an all-out effort to increase federal spending for social welfare programs.

After an hour meeting with Carter, caucus members emerged from the White House to issue some of their strongest statements to date in what has become a running battle with he administration over the fiscal 1980 budget.

"We explained to the president that we are going out and mobilizing our tropps," said Rep. Cardiss Collins (D-Ill.), who heads the caucus. "We laid down the gauntlet, so to speak. We are not going to sit back and take these budget cuts.We're not going to say we did the best we could. We're going to mobilize."

The White House response to the challenge was equally determined.

"It's clear this is an area of disagreement," said presidential press secretary Jody Powell. "We intend to make every effort to hold the line on the budget. The debate will be settled by the political process."

Presidential aides were concerned enough about the meeting to summon reporters to tell the White House side of the dispue immediately after Collins spoke.

One official said the meeting had not been angry, but that the president had "made it clear he has no apologies" for the shape of the budget he submitted to Congress in January.

While saying that Carter sympathized with the concerns of the caucus members, the official also conceded that there are serious differences, particularly over the president's recommendation to increase defense spending by 3 percent above the inflation rate.

Carter meets regularly with the Black Caucus, with which he has often had a shaky relationship. That relationship grew even more stormy late last year, as the president repeatedly promised a "very tight" budget to combat inflation and the caucus urged him to spare social welfare programs from deep spending cuts.

White House officials said specific budget items were not discussed during the meeting, which lasted almost twice its scheduled length. But, outside the White House, caucus members cited jobs and housing programsas two areas of concern to them.

D.C. Del. Walter Fauntroy (D), the city's nonvoting representative in Congress, said the Black Caucus plans to ask governors and mayors around the country to assess the impact of the administration's bedget cuts on their states and cities. He said the caucus will then take this information to Congress in an attempt to win appropriations increases for some domestic programs.

Caucus members made it clear that they are most angered by the proposed increase in defense spending, which Rep. Ranald V. Dellums (D-Calif.) called "potentially dangerous and intolerable."

Collins said the president told the group he hoped they could work together. She said while she thought this was possible, "We are not going to lose sight of our goals."