Vice President Mondale will head a task force on District of Columbia problems at the personal request of President Carter, the Vice president's office announced yesterday.

Mondale's selection seems sure to guarantee serious cooperation with the task force by government agencies, and to assure that the task force's eventual recommendations will have a high visibility and chance for acceptance.

Formation of the task force was suggested March 15 at a White House meeting of the President and Vice President with members of Congress who serve on committees dealing with District matters. The suggestion was made by Chairman Charles C. Diggs Jr. (D-Mich.) of the House District Committee.

The President agreed, and asked for a prompt report - within two or three months - on the capital city's pressing problems and ways the federal government can help deal with them.

An aide to the Vice President said Carter asked Mondale last week to take the task force chairmanship.

Martha (Bunny) Mitchell, the President's special adviser on District matters, said a staff meeting had tentatively been scheduled for today to discuss the size of the task force and to move toward choosing those of its members who will represent the executive branch of government.

As discussed at the March 15 meeting, the task force also would include members of Congress, representatives of the District government and possibly nongovernmental community leaders.

Among subjects discussed at the White House meeting for consideration by the task force were the possible setting of a formula for setting the annual federal payment in lieu of taxes to the District government, funding the city's $1.4 billion of pension obligations, the payment of $19.8 million of bonds that were sold to pay for building the Robert F. Kennedy Stadium, completion of the Metrorail system and Pennsylvania Avenue redevelopment.