The House Appropriations Committee yesterday approved a Pentagon spending bill that sets up another fight with the White House over four Democratic-backed restrictions on President Reagan's nuclear arms-control policies.

Rejecting Republican pleas that the restrictions would hurt ongoing U.S.-Soviet arms control talks, the Democratic-controlled panel sent the bill to the floor on a voice vote. That came after the committee rejected a GOP attempt to strip the arms-control restrictions from the bill.

The measure is likely to come up on the House floor next week, when the chamber begins considering an omnibus spending bill to finance federal agencies, including the Pentagon, for which individual appropriation bills have not been approved.

The four restrictions would halt final-stage tests of antisatellite weapons, require adherence to the unratified SALT II nuclear arms control treaty, halt all but the smallest tests of U.S. nuclear weapons and block tests of Strategic Defense Initiative (SDI), or "Star Wars," missile defense systems that would violate the 1972 Antiballistic Missile Treaty.

The four restrictions are part of a bill appropriating $268 billion for the Pentagon for the fiscal year that began Oct. 1.

The restrictions were contained in a separate bill approved by the House last May, a measure which authorized defense spending for the current fiscal year. All four were added on the floor on votes which went largely along party lines in the Democratic-controlled House.

In the complicated congressional budget process, separate bills are needed to authorize spending and then to appropriate funds.

The Senate later added two of the restrictions, requiring compliance with SALT II and blocking some SDI tests, to its version of a bill authorizing the Pentagon budget.

A House-Senate conference committee is attempting to reconcile the two authorization bills. Reagan has threatened to veto any bill that contains the restrictions.