A House-Senate conference committee has agreed to require the Pentagon to give a new kind of notice to Congress any time there is a cost overrun of 15 percent or more on a major weapons system.

Championed by Sen. Sam Nunn (D-Ga.) and passed by the Senate on a vote of 96 to 0, the requirement ran into opposition from the Pentagon and from House conferees when it came to hammering out the compromise defense authorization bill for fiscal 1982. But Nunn ultimately prevailed in the conference which ended Thursday night.

In the bill to be recommended to the House and Senate for final passage, the Pentagon's own estimates of March, 1981, would be the starting point for measuring overruns.

If the cost of a weapons system ran past these March estimates by 15 percent or more, a detailed explanation would have to be sent to Congress within 30 days. Otherwise, the money for the guilty program would be frozen. The idea is to create a kind of early warning system on overruns, with a device that will make the Pentagon both disclose and justify them.

Adoption of the Nunn amendment is another sign of nervousness among lawmakers over the fact they are raising the military budget while cutting domestic programs; they do not want to be thought tolerant of waste at the Pentagon. Chairman John G. Tower (R-Tex.) of the Senate Armed Services Committee acknowledged that defense money requests will run into this attitude from now on in Congress.

"We're going to have to justify everything," said Tower of the programs in the fiscal 1982 defense budget. But he predicted President Reagan's revised defense budget would survive pretty much intact after floor fights over the bills actually appropriating money to the Pentagon.

The House and Senate Armed Services committees set money ceilings for most Pentagon programs, not the actual amounts to be appropriated. The compromise bill approved by the conference authorizes $130.7 billion in budget authority, which is the right to spend money out in the future. Tower said this is a $7.3 billion reduction in authority to achieve the $2 billion cut in actual spending this year that Reagan had requested.

Tower said that the B1 bomber and MX land-based missile are likely to generate the hottest fights when it comes to appropriating money for them later on in the congressional session.

"There are doubts about the B1," Tower acknowledged. He said that he personally favored the plane and warned that the alternative of waiting for the more advanced "Stealth" radar-evading bomber would be a gamble.

The Senate Armed Services Committee is much less supportive of President Reagan's plan to deploy MX missiles in existing Minuteman and Titan silos. Tower had strongly endorsed the Air Force plan to move the MX missile from one shelter to another to make it difficult for the Soviets to target.

"The big question is what is the cost profile of hardening silos," Tower said of Reagan's MX-basing scheme. The Air Force has told the Senate that it may cost as much as $7 billion to fortify existing silos against nuclear attack before the MX is inserted into them.

The authorization bill contains $2.1 billion for the B1 bomber, a reduction of $300 million, and $1.9 billion for the MX, with $300 million of it a downpayment for basing work.

In one of the behind-the-scenes battles waged during the long conference on the defense authorization bill, Nunn and several other senators tried to add language subjecting the B1 and MX programs to a vote of disapproval by either the House or the Senate. The House insisted that such disapproval would have to be done through a resolution passed by both houses, not just one. The language in the compromise bill sets Nov. 18 as the deadline for disapproval of the MX and/or B1 by a vote of both the House and Senate.