President Carter, bowing to strong resistance in Congress, yesterday withdrew his nomination of Donald L. Tucker, speaker of the Florida House of Representatives, to be vice chairman of the Civil Aeronautics Board.

The action came in the face of nearly solid opposition in the Senate Commerce Committee following a staff investigation that some members said allegedly linked Tucker with a series of questionable financial dealings.

Commerce Committee members reportedly made it clear to the White House that if the Tucker nomination were pressed it would be rejected outright by the panel. Some warned the issue could result in a major confrontation.

News of the decision came first from Tucker, who held a mid-morning news conference in Tallahassee, Fla., to announce he had asked the President to withdraw his name from consideration.

The action followed a weekend of negotiations between Tucker and Robert J. Lipshutz, the President's counsellor, in which Lipshut, reportedly pressed the Florida legislation to step down voluntarily to avoid any embarrassment.

Carter nominated Tucker for the post in June, in part as a political reward. The House speaker had been the first major Florida political figure to endorse the Carter campaign effort in that state's 1976 primary.

The Commerce Committee never publicly spelled out what it had uncovered about Tucker's financial dealings. The investigators' report was delivered verbally to only a few members, and the documents were locked in a safe.

However, sources on the panel indicated some of the findings pointed to possible dealings between Tucker and Robert Vesco, the financier now living in Costa Rica, and alleged questionable political contributions.

Sen. Howard W. Cannon (D-Nev.), chairman of the panel's aviation subcommittee, met privately with Lipshutz three weeks ago to lay out the staffers' findings. The White House had delayed any action until yesterday.

Tucker did not respond to a telephone inquiry yesterday. However, he told the press conference the Florida senatorial delegation had advised him that "even though I can clearly repudiate all allegations, there is no way I can receive a fair hearing" from the Commerce Committee.

He said Sen. Richard B. Stone (D-Fla.), also from Tallahassee, had told him that "even without hearing my testimony, many of the members are already committed against my nomination."

Tucker's withdrawal sparked expressions of relief from some members of the Commerce Committee, whose Democratic majority obsiously had been trying to avoid a direct clash with the White House in the wake of the Lance affair.

Immediately after Tucker's announcement, Cannon issue a statement calling the move "a wise decision." He urged Carter to reconsider the early retirement of G. Joseph Minetti, a current member of the Commission, who has reached the age of 70. Mr. Minetti could retain his seat on the board under a presidential release.

As in the case of the Lance affair, Carter did not concede any wrongdoing on the part of his nominee. His letter to Tucker, made public by the White House, said only that "I understand the reasons which you have given for your request."

The President added that "I have complete confidence in your competence and integrity, and regret that our nation will be deprived of good services."

In a briefing yesterday, White House officials told reporters Tucker had asked that his name be withdrawn on Friday, following a Thursday meeting with Lipshutz, Carter adviser Charles Kirbo and Hamilton Jordan, the President's unofficial chief of staff.

Lipshutz said yesterday that, in part as a result of the Tucker experience, the White House now would ask the FBI to evaluate presidential nominees in its routine background checks on them, rather than simply report its findings without comment.