The House joined the Senate yesterday in rejecting a proposed $354 million arms sale to Saudi Arabia by a decisively larger margin than the two-thirds vote necessary to override a veto of the disapproval resolution by President Reagan.

The 356-to-62 vote was immediately hailed as "veto proof" by Rep. Mel Levine (D-Calif.), who led House opposition to the sale. He predicted that the Senate, which voted 73 to 22 Tuesday to reject the sale, would also override a veto, marking the first time in history that Congress blocked a proposed arms sale.

In a statement, White House spokesman Larry Speakes said, "It is the president's intention to veto this resolution and to work actively with members of both houses of Congress to sustain that veto."

The House vote exceeded by 67 votes the 289 necessary to override a veto. In the Senate, which would be first to vote on a veto, sale opponents mustered six votes more than the 67 necessary to override the president.

Reagan had vowed at a news conference in Tokyo yesterday after the Senate action that he would confront Congress on the issue when "the old man gets home." But the extent of congressional opposition to the sale made it clear that the administration faces an enormous task in sustaining a veto.

"I think it's doable, but I think it's very tough," a White House official said of prospects for the sale. He said the main administration effort would be made in the Republican-controlled Senate, where "we clearly have a better chance of sustaining a veto."

Rejection of the Saudi arms sale also deepened the administration's foreign-policy problems on Capitol Hill. In addition to the immediate task of rescuing an arms package for a key Middle Eastern country, the administration faces another difficult House test next month on its long-stalled policy to pro- vide military aid to Nicaraguan rebels.

The margins by which the Saudi sale was rejected exceeded the wildest hopes of opponents in both chambers. Opposition steadily mounted in recent days, with some lawmakers linking this to Reagan's harsh antiterrorist and anti-Libyan rhetoric over the last few weeks.

Throughout the two-day congressional debate, opponents repeatedly cited Saudi Arabia's public condemnation of the U.S. air raid on Libya last month as proof that the Saudis worked to undermine U.S. interests in the Middle East.

"I think Libya broke it," Rep. Barney Frank (D-Mass.) said. "You can't whip up as much anti-Libyan sentiment as he [Reagan] has and not have it bite" you.

The House vote also clearly reflected increasing congressional concern about international terrorism and the possibility that U.S. weapons could fall into the hands of radical terrorist groups.

The proposed package includes Sidewinder air-to-air and Harpoon antiship missiles and 800 Stinger antiaircraft missiles. The Stinger is a shoulder-fired weapon that Rep. John F. Seiberling (D-Ohio) and others described as "made to order for terrorists."

Levine said "the whole question of terrorism in the region," combined with Saudi support for Libya and inclusion of Stingers in the package, played a key role in building the huge House margin against the sale.

He also suggested that the administration may have underestimated the extent of congressional opposition after Israel and the main pro-Israeli lobbying organization, the American Israel Public Affairs Comittee, decided not to oppose the sale actively.

A White House official, who asked not to be identified, denied that the administration underestimated its task but confirmed that the vote reflected a growing anti-Arab sentiment in Congress. "It got to be a very emotional vote," the official said. "Some guys seemed to view it as a referendum on Arabs in general."

"I can't say the president's rhetoric backfired," the official added, "but the Saudi public reaction to the [raid] on Libya really turned some people off who in the past have really been supportive."

In the House vote, 225 Democrats and 131 Republicans, majorities in both parties, opposed the sale. The emotional issue turned normal legislative alliances topsy-turvy, with such conservative Republicans as Vin Weber (Minn.) and Robert K. Dornan (Calif.) opposing the administration, while such liberal Democrats as Lee H. Hamilton (Ind.) and Gerry E. Studds (Mass.) backed the president.

Supporters argued that the sale posed no threat to Israel and involved only resupply of weapons already in the Saudi arsenal, and that the Saudis need the weapons for defensive purposes.

Rejection of the sale, Rep. Robert J. Lagomarsino (R-Calif.) said, "will signal that the United States cannot distinguish between radical Arab states that practice terror and moderate Arab states that seek protection."