The Republican-controlled Senate Appropriations Committee yesterday approved a $3.9 billion program for jobs and other relief for recession victims that falls $1 billion short of a similar measure approved last week by the Democratic-controlled House.

Under pressure from the White House to reduce the spending even further, committee Chairman Mark O. Hatfield (R-Ore.) indicated that he will push on the Senate floor later this week to strike out another $373 million, mostly from construction and repair at veterans' hospitals.

While the Senate bill is smaller than its House counterpart, it channels more of its funds toward states with the highest unemployment rates.

With the major exception of health care, which the House funded more generously, the Senate bill is also weighted more toward social services and less toward construction projects.

As recommended by Hatfield, it was stripped of some House-approved provisions that triggered objections from President Reagan, such as $200 million in small business loans, although sources said the White House still had problems with Hatfield's version.

While smaller than the $4.3 billion proposal that Reagan offered last month under pressure for a jobs compromise from both Republicans and Democrats, the Senate bill does not count some already appropriated funds that Reagan included in his spending total.

Hatfield had been prepared to ask for committee approval of his cuts, but backed off when he discovered that no Democrats were present. He said he would offer the cutting amendment formally when the Senate as a whole begins action on the measure, probably Thursday.

Congress is under pressure for quick action on the measure because the recession-relief package has been included in legislation to continue funding of unemployment benefits after existing funds for the program dry up. Hatfield said yesterday that unemployment funds will run out next week.

In addition to $5 billion to continue funding unemployment benefits, the bill also includes $5.7 billion for farm price supports, which, like unemployment benefits, have been strained by the recession.

Like the committee-approved House version of the measure, which was somewhat sanitized during debate on the floor, the Senate draft of the bill earmarks big chunks of money for construction and transportation projects in areas represented by members of the Appropriations Committee.

Taking note of the large number of military housing projects designated for Georgia, the home state of Sen. Mack Mattingly (R-Ga.), chairman of the military construction subcommittee, Sen. Thomas F. Eagleton (D-Mo.) urged the committee to get rid of some of the "pork," as he put it.

In all, Georgia would get about $18 million of $100.5 million designed for military housing.

When Hatfield chided him about military construction projects in Missouri, Eagleton grumbled, "Take 'em all out . . . . What I'm trying to get here is truth in labeling." Others disagreed and he got no support.

"This is not pork . . . . They're projects that have been on the waiting list for a long time," said Sen. Ted Stevens (R-Alaska).

Eagleton also lost in an effort to restore $200 million that the committee took out of the House bill for health care. Several members, including Sen. Lowell P. Weicker Jr. (R-Conn.), said the jobs bill was not the proper vehicle for health spending but indicated that they would support Eagleton's proposal later.

In relatively small additions to the measure, the committee approved $3.7 million for radar to help the Customs Service apprehend drug smugglers and $5 million for jobs for the handicapped. It also agreed to reject all of Reagan's proposed deferral of $229 million for mass transit, instead of a smaller amount that had originally been recommended.

In targeting funds for high-unemployment states, the committee rejected a House formula designating about $1.8 billion for hardest-hit areas and substituted one that would allocate $2.1 billion based on unemployment rates and favor the 15 states with the highest jobless rates.