One day after the House and Senate approved defense authorization bills that provide a go-ahead for the huge new MX intercontinental missile, Democrats yesterday picked up a crucial Republican vote to force a Senate Foreign Relations Committee meeting on a proposed nuclear freeze.

The session, scheduled for Tuesday, was forced after committee member Larry Pressler (R-S.D.) joined all the panel's Democrats in invoking a rule under which a committee majority can require a meeting, even over the objection of its chairman.

After postponement of several earlier sessions, Committee Chairman Charles H. Percy (R-Ill.) had scheduled a meeting for Sept. 20 and resisted Democratic pressure to move up the date. Percy was in Illinois yesterday and unavailable for comment.

Pressler, chairman of the panel's subcommittee on arms control, said he signed the Democrats' letter because of "impatience" with the administration over arms control, especially over the "build-down" concept under which two older nuclear warheads would be retired for each new one that is added.

"I've just grown increasingly frustrated with the slowness of the thing," Pressler said yesterday.

Pressler said he voted for the MX Tuesday "in the context of an arms control chit" and that he felt that committee consideration of the freeze, even though he does not support it in its current form, might prod the administration to move more rapidly in developing a build-down bargaining position.

Unless the administration acts in the meantime, Pressler added, he will not vote for MX appropriations this fall.

The proposal before the committee, drafted by Sens. Edward M. Kennedy (D-Mass.) and Mark O. Hatfield (R-Ore.), calls for a mutual and verifiable freeze of American and Soviet nuclear arsenals at current levels. A somewhat modified version of the proposal was adopted earlier in the year by the Democratic-controlled House.

While the Kennedy-Hatfield proposal is not expected to pass the Republican-controlled Senate, freeze backers focused on committee action as a first step, and Sen. Nancy Landon Kassebaum (R-Kan.) indicated she would join Pressler and the Democrats in sending the issue to the Senate floor.

Passage of the defense authorization bills, including $4.6 billion for MX-related costs over the next year, drew praise yesterday from President Reagan, who got most of what he wanted in the measures.

"It is good news for all Americans that the House and Senate have again demonstrated bipartisan unity in pursuit of two vital national goals--strategic modernization and arms control," he said in a statement.

After a marathon session that lasted until early yesterday, the House voted 305 to 114 for a $187.3 billion defense authorization for fiscal 1984. It includes a 4 percent military pay raise starting in January as well as most of the new weaponry that Reagan wanted.

Earlier, the Senate, voting 83 to 15, approved a $200 billion measure that also includes military construction and nuclear weaponry. The Senate bill provides a 4 percent pay raise starting in April unless Congress approved an earlier pay raise for civilian workers. These and other issues will be resolved in a House-Senate conference.