The D.C. City Council sent next year's proposed city budget to the White House yesterday after pointedly ignoring Mayor Marion Barry's vetoes of several items it contains.

The council's action, taken after only a brief explanation and no debate, was another step in its attempt to gain more control over the city's pursestrings.

While the total amount of the items vetoed by the mayor -- $601,100 -- was a minor part of the city's proposed $1.5 billion spending package for the 1981 fiscal year, the council's action represented a fundamental challenge to the mayor's role in the budget-making process.

Under the Home Rule Charter, the mayor initiates each year's proposed budget and submits it to the council for review. The council may make changes. After the council completes action, it sends the revised budget back to the mayor.

Barry, following a process routinely used by former mayor Walter E. Washington, used his power to veto council changes in an attempt to restore $601,100 to pay for an array of programs the council had produced.

James M. Christian, the council's chief lawyer, said his office reviewed this process and decided it was wrong. He advised Council Chairman Arrington Dixon to ignore the mayor's actions.

Fundamentally, Christian told a reporter, his opinion and that of others on his staff is than "the mayor can only exercise his veto on items that are actually contained in the (council's) budget act."

Under this legal interpretation, Christian said the mayor may exercise his veto to eliminate or reduce items that had been approved by the council, but may not increase them.

Gladys Mack, the mayor's budget director, said she has asked the corporation counsel's office to explore the city council's action.

She said she had been warned that the action was coming, and yesterday sent a package of budget amendments to the council that would restore the $601,100 to the budget. If the council approves, those would be sent along to the White House to be added to the document that will be transmitted to Congress.

By voice vote, the council overrode the mayor's vetoes of two items in the budget dealing with details of municipal housekeeping. These did not involve any changes in the dollar amount of the budget.

At yesterday's meeting, the last in 1979, the council also approved the creation of a task force to conduct an 18-month study of the structure and functions of the Board of Elections and Ethics and to recommend changes. The study was proposed by council member William R. Spaulding (D-Ward 5).