President Reagan bowed to pressure from Congress yesterday and offered House Democratic leaders a $4.3 billion jobs and recession relief package that includes new federal construction projects and a sizable amount of humanitarian relief for the jobless.

House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) hailed the package as "progress in meeting the country's economic emergency" and promised to take it to House committee chairmen and Senate Democrats in the next few days before reporting back to the president.

The package was offered at a secret meeting yesterday afternoon in O'Neill's office that included the speaker, Office of Management and Budget Director David A. Stockman, White House chief of staff James A. Baker III, House Majority Leader James C. Wright Jr. (D-Tex.) and House Democratic Whip Thomas S. Foley (D-Wash.).

In a carefully worded statement suggesting that Reagan and Democrats are near agreement on the package, O'Neill said it moves "significantly in the same direction" as the $5.4 billion anti-recession proposal that Reagan threatened to veto during the lame-duck session of Congress last year.

How much of the $4.3 billion is new money and how much is a speedup of existing programs was not immediately clear.

Sources said the package includes a sizable amount of humanitarian aid, such as food and shelter, for those hurt by the recession, including new money for child nutrition. It also would accelerate some federal construction projects and possibly provide money for new projects.

The sources said the package does not contain the kind of public works jobs that Reagan has objected to as "make work," but would provide additional money for community development block grants, which go to cities for housing and urban development needs. Stockman yesterday defended Reagan's new budget against charges that it is unfair to the poor. Details on Page A4.

The White House had no comment on the package, but one administration official, referring to the initial congressional reaction, said, "From what they say, it looks good."

The proposal was greeted warmly by the House Democratic leaders.

Wright said he was "very enthusiastic" and "agreeably surprised at the distance the administration has come to embrace and accept the major components of our jobs initiative last December."

Foley, who has been coordinating recession relief efforts for the House Democratic leadership, said the package was a "very constructive and positive development."

But he cautioned that it might not please everyone, including Democrats who want to go further.

"There are people in the Democratic Party who feel even an initial effort should be much larger," Foley said. "But if we can agree quickly on an early delivery of job assistance to substantial numbers, that is a first step which doesn't bind anybody."

Foley argued that if the Democrats delay accepting the package, "I'm not comfortable with a prolonged debate, so that winter shelters become available in July and summer jobs in October while Congress" argues about which way to go. In his statement yesterday, O'Neill said the president had promised him in a Jan. 31 meeting to direct Stockman to find areas where government spending could be used to create more jobs.

"The president has kept his promise," the speaker said. He said chief of staff Baker and Stockman had "brought me a number of immediate approaches for creating jobs and relieving the human suffering caused by the current economic situation."

O'Neill said that in addition to reviewing the package with Senate Democrats, he would take it on Monday to the House Democratic Steering and Policy Committee. There was no immediate word on how Senate Republicans would receive the proposal.

Foley said the package came about because both the White House and the House Democratic leadership realized that a prolonged debate would delay the needed relief.

"There's no way we can pass a bill without a president's signature or being able to override a presidential veto," he said. "It does us no good to have a bill that will just pass the House. That doesn't provide a single meal, a single blanket, or a single job."

Foley said it was important that Congress "avoid the struggle" and "get immediate assistance out to real people," while not foreclosing the right of those who want a larger package enacted to offer it later.

At a press luncheon yesterday, Stockman said "the disinflationary process is over."

Asked what inflation and unemployment rates the administration would like, Stockman indicated that inflation should be held below 5 percent. Unemployment of about 6 percent is "probably a reasonable and realistic target," he said. It is "probably the best that you can do in current" economic circumstances.

Also yesterday, Reagan told a group of businessmen that he talked with Federal Reserve Chairman Paul A. Volcker, who assured him the central bank would take a "middle course" in controlling the money supply that would help recovery while not reigniting inflation.

White House aides said later that Volcker met with Reagan on Friday in the Oval Office. Robert Thompson, chairman of the Chamber of Commerce of the United States of America, said that Reagan told the group "he felt Volcker was fully aware of the dangers of reigniting inflation and he intends to take a middle course which he felt could lead to a full recovery without further inflation."

Earlier yesterday, Reagan authorized the Justice Department to appeal a federal court ruling that has sidetracked administration-backed changes in the Davis-Bacon construction wage law. The decision was made at a meeting of the Cabinet Council on Economic Affairs.