The House approved a $9.4 billion suppplemental appropriations bill for the remaining three months of fiscal 1987 yesterday, sending the measure back to the Senate for possible final enactment later this week.

The House-passed version of the legislation included a compromise plan for drug testing of federal employes in "sensitive" jobs and a proposal to settle a House-Senate dispute over the future of the new U.S. embassy in Moscow by putting off any decisions until at least Nov. 1.

The original House version of the bill would have banned expenditures to implement President Reagan's executive order of last September requiring drug testing of certain federal employes. The Senate's supplemental appropriation legislation would allow drug testing under certain conditions.

The compromise that emerged from a House-Senate conference committee would expand the conditions under which drug testing would be allowed. Those conditions include requirements for uniform testing plans by federal agencies, uniform certification standards for those who conduct the tests and full access to the test results for employes.

The House accepted the compromise after defeating, 343 to 77, a Republican-led attempt to adopt the weaker Senate conditions.

The main issue that remains between the Senate and the House involves the uncompleted Moscow embassy, which has been described as riddled with Soviet intelligence-gathering devices.

The Senate added an amendment to its version of the legislation allowing expenditure of funds only to demolish the embassy. The House countered yesterday with a proposal to ban any spending on the embassy and to prohibit Soviet diplomats from occupying their new embassy in the Mount Alto section of Washington until Nov. 1.

"At this point, we should put everything on hold," said Rep. Neal Smith (D-Iowa) in urging the delay to give the administration and Congress more time to decide the Moscow embassy's future.

Former defense secretary James R. Schlesinger, who was appointed by Reagan to investigate the embassy controversy, told congressional committees Monday that that the facility could be salvaged if the top three floors are demolished and rebuilt and a new annex is constructed for the most sensitive embassy operations.

More than half of the $9.4 billion in the measure would go to the Commodity Credit Corp., which has run out of money for loans to farmers. The bill also contains $300 million in aid for Guatemala, Costa Rica, Honduras and El Salvador; $747 million for military programs; $287 million for Pell grants to low-income college students, and $77 million for programs to counter the spread of the acquired immune deficiency syndrome virus.

In addition, the measure would appropriate $355 million in emergency aid for the homeless. Later last night, the House approved, 310 to 115, separate legislation authorizing the emergency homeless aid program that the Senate approved last week.

During the conference committee deliberations, the House agreed to drop two arms-control provisions opposed by the Reagan administration but have been added to other bills moving through Congress. The provisions would require the administration to comply with the limits on weapons deployment in the unratified SALT II arms-control treaty and would prohibit tests of nuclear devices of more than one kiloton so long as the Soviet Union complied with the test ban.

House Speaker Jim Wright (D-Tex.), calling on Reagan to seek an accommodation with Congress on arms-control policy, said deletion of the two amendments from the appropriations bill should not be interpreted as a reversal of the House's position.