House passed yesterday what chief sponsor called a "diplomatic responsibility bill," eliminating this country's near total grant of legal immunity to foreign embassy personnel setting new rules subjecting them to American laws.

Following the House action, a spokesman for the Senate International Operations Subcommittee said its chairman Sen. George S. McGovern (D-S.D.), is ready to move as quickly as possible toward enacting the measure into law. He said a hearing probably will be held in September.

Yesterday's action was unanimous on a voice vote. Rep. Dante B. Fascell (D-Fla.), chairman of the House International House Operations Subcommittee and the bill's chief sponsor, assured House members that its passage would not invite reprisals by other nations on American diplomats.

The original version of the bill was introduced by Rep. Joseph L. Fisher (D-Va.) to force embassy personnel to be responsible for claims resulting from automobile accidents and to pay traffic tickets. Diplomatic immunity has been claimed in several well publicized automobile accident cases that caused injuries or deaths in the Washington area.

Fisher hailed yesterday's action. He said Sen. Charles McC. Mathias Jr. (R-Md.) has agreed to push the measure in the Senate.

The new measure keeps full immunity from American judicial processes for ambassadors and other top-ranking embassy officials, but withdraws that right in varying degrees from lower-ranking embassy personnel, their families and household servants.

In Washington area, the number of persons covered by broad diplomatic immunity would be reduced from an estimated 6,000 to about 2,200, plus family members.

The House-passed measure would repeal a law passed by Congress in 1790 - a decade before Washington became the nation's capital - that grants full immunity from American laws to almost everybody connected with any embassy.

Full immunity would be replaced by various degrees of immunity agreed upon by the United States and other nations at an international meeting at Vienna in 1961.

Under the new arrangement, top-ranking diplomats and their families would keep full immunity. Lower-ranking embassy personnel would be immune from criminal prosecution but could be sued for actions they do as private individuals. Household servants would be stripped of all legal immunity.