Responding to pressure from numerous senators, Secretary of State Cyrus R. Vance said yesterday the Carter administration will seek a substantial increase in the 1981 defense budget to make good on its year-old commitment to NATO to increase defense spending by 3 percent a year after inflation.

Testifying before the Senate Armed Services Committee on the strategic arms limitation treaty, Vance acknowledged that the effects of unexpectedly high inflation plus congressional cuts have prevented the administration from meeting the 3 percent committment this year. "It is essential that we carry out that committment," Vance said.

According to the calculations of an aide to Sen. Sam Nunn (D-Ga.), who has demanded increased defense spending as the price of his vote for SALT II, the administration would have to add $4 billion or $5 billion to the fiscal 1981 defense budget to reach the 3 percent target, on top of increases already projected.

Vance told the committee that a general consensus on the need for more military spending is "a benefit that will come out of those hearings."

Last week Nunn recommended a real annual increase of 4 to 5 percent in the defense budget for the foreseeable future. The White House is hopeful that it can find a formula for increased spending that will satisfy Nunn and convert him to an active supporter of the new treaty.

Many other senators have echoed Nunn's position, usually with less precision. Indeed, more defense spending has emerged as the dominant theme of the SALT hearings, enunciated first by Vance and Defense Secretary Harold Brown at the opening of hearings in the Foreign Relations Committee three weeks ago.

In his testimony yesterday, Vance went over ground covered previously either in the Armed Services or Foreign Relations Committee's hearings. The only electricity of the day came in two cross-examinations of the secretary of state by Sen. Henry M. Jackson (D-Wash.).

Jackson challenged Vance on the administration's claims for the "new type" definition in the new Treaty. This limits both superpowers to a single entirely new type of land-based rocket during the life of the treaty (which expires at the end of 1985), but permits replacemens of existing rockets provided they don't change from existing models in certain key characteristic by more than 5 percent.

Jackson claimed that this provision is so loosely drawn that the Soviets will be able to deploy four new rockets to replace all their existing models.

If so, Vance replied, "that would not change militarily the position. It would make no significant difference."

Then Jackson listed improvements that could legally be made in Soviet rockets under the treaty, noting that the accuracy of warheads, effeciency of rocket engines and fuels, recket electronics and command and control facilities for the rockets could all be emproved without any limitations. Jack asked Vance whether any of these would be militarily significant, and Vance acknowledged that accuracy and explosive power both would be.

Some members of the official entourage that accompanied Vance and sat behind him in the enormous Senate caucus room as he testified squirmed during Jackson's questioning. Several scribbled notes to pass up to the secretary suggesting different answers to the veteran hard-liner's queries.

But only later, when Sen. John C. Culver (D-Iowa) gave Vance a sympathetic line of questions on the same subjects, did Vance finally get the Administrtion's position on this issue on the record. (Last week, Brown had also given the administration view.)

Culver elicited from Vance confirmations that with the accuracy, explosive power and efficiency that the Soviet's land-based missiles buried in concrete- and -steel silos. Therefore, Culver said and Vance agreed, improvements in these areas would not give the Soviets any significant new military capability.

However, Culver said and Vance again agreed, the new treaty's limits on the number of warheads a single missile con carry and on the weight of a missile's payload do prevent the Soviets from attaining added capability that could be significant -- the ability to "saturate" a new mobile U.S missile system.

In other words, with a large enough number of accurate warheads, the Soviets could neutralize even a mobile missile system, but with the SALT II limits on warheads that Soviets could not acumulate that many.

Vance's entourage smiled approvingly at the completion of Culver's questions. But later Jackson returned to the subject, and again got Vance to change his testimony with another acknowledgement that further improvement in the explosive power of Soviet warheads "does have an important impact."

On another subject, Vance said he thought it unlikely that the NATO allies would agree to station new strategic weapons -- either a medium-range ballistic missile or land-based cruise misiles -- on their territory if the Senate rejects SALT II. Modernization of NATO forces and future good relations within the alliance depend on approval of the treaty, he asserted.