More than 10,000 of 19,029 foreign embassy personnel in the District will lose some measure of diplomatic immunity from suit under bills passed separately by the House and Senate, the State Department said yesterday.

The bills would make, for the first time, 10,948 foreign embassy employes and servants subject to some degree to the American civil litigation process. The bills would permit 2,309 diplomats and 5,772 family members diplomats to retain their full immunity from both criminal prosecution and civil suits.

The Senate passed the bill Thursday. The House passed a similar bill last year. Both bills would require diplomats and their families to carry automobile liability insurance so that victims of automobile accidents they cause can collect damages. Under existing law, which does not require insurance, accident victims of foreign embassy personnel have sometimes not been compensated for injuries.

The only difference between the bills is that the Senate version include a clause requiring the diplomats' insurance companies to pay accident victims if the accident was the fault of the diplomat or a family member.

Previously, some insurance companies refused to pay damages to victims of diplomats' accidents on the grounds that diplomats have immunity from suit. A spokesman for Rep. Joseph Fisher (D-Va.), who cosponsored the House bill, said the House will consider amending its bill in September to include the Senate provision. An agreed bill will then go to President Carter for his signature.

"We've been pushing and promoting this bill for years," said a State Department spokesman. "Other countries took immunity away from the staffs of U.S. diplomats years ago. We're one of the last countries to chip away at immunity."

In the early 1960s the United States and 123 other countries signed the Vienna Convention, a treaty that drastically curtailed the immunity granted to all foreign embassy personnel. It made the degree of immunity commensurate with the rank and duty of the employe.

The Senate and House bills would translate the provisions of the Vienna Convention into law in this country, supplanting a 1790 law that gave full immunity from civil suits and criminal prosecution to everyone attached to foreign diplomatic missions in this country.

Diplomatic immunity was orginally invoked to protect representatives of a government from intimidation - or from trumped-up charges - in the country in which they were stationed, according to a State Department spokesman.

Because most other countries have adopted the terms of the Vienna Convention, the staffs of U.S. diplomats abroad have already had their immunity curtailed. The State Department said that consequently the Senate and House bills would not result in relaliatory measures against U.S. staffs abroad.

Both bills permit the president to reach separate agreements with other countries on an individual basis regarding immunity. It is expected, for instance, that the president will sign an executive order permitting the staffs of Soviet Union diplomats to have the same full immunity from criminal and civil suit as American diplomats and staffs presently have in the Soviet Union.

In addition to the 8,081 diplomats and family members who will retain full criminal and civil immunity, 2,877 members of diplomats' administrative and technical staffs will retain full criminal immunity, but they would be immune from civil suit only when acting in official capacities.

The 7,192 family members of administrative and technical staff personnel will also retain full immunity from criminal suit, but they would have no immunity from civil suit.

Chauffeurs, janitors and other service personnel - all 273 of them - will be protected from criminal and civil suit only if they acted at the directive of their embassy.

The 606 private domestic servants and families of chauffeurs, janitors and other service personnel would be considered ordinary citizens and would not have any immunity.