The House Armed Services Committee voted yesterday to cut $2 billion from President Reagan's budget request for "Star Wars" research on antimissile defenses, congressional sources said.

The decision came as the panel met behind closed doors to write its version of a Defense Department budget bill for the fiscal year starting Oct. 1.

Reagan sought $5.4 billion next year for the program, known formally as the Strategic Defense Initiative, compared with a current budget of $3 billion.

The Democratic-controlled House panel cut the SDI budget to $3.4 billion, said the sources. That vote approved the SDI budget passed by one of the panel's subcommittees last week, the sources noted, following defeat by the full committee of four other SDI budget proposals, all smaller than Reagan had asked.

The Republican-controlled Senate Armed Services Committee, in its version of a Pentagon budget bill, last week approved $3.95 billion for the SDI.

The decisions are the first major steps in the lengthy congressional budget process. The committee bills will go to the floor of each chamber next month and differences between the two versions that pass will be ironed out in a conference committee.

Also yesterday, the House panel gave the final go-ahead for the Navy's "home-port" plan, voting to release $76 million in 1986 funding to begin construction of ports at Staten Island, N.Y., and Everett, Wash.

The Senate Armed Services Committee approved a similar measure earlier this month.

The Navy contends that dispersal of its fleet among more ports is necessary to improve military readiness and flexibility.

Critics of the idea say the spending is unnecessary and that the Navy could save millions of dollars by enlarging current ports to meet its needs.