After nearly two years of sometimes strained relations between Washington and strategically important Norway, the new Conservative government has changed the tone of Norwegian foreign policy, emphasizing strong support for the NATO alliance and close relations with the United States.

Prime Minister Kaare Willoch's government has abandoned the previous Labor government's campaign for a Nordic nuclear-weapons-free zone and ended disagreements with the United States about NATO nuclear strategy.

Since taking office in October, the Willoch government has acted also to increase Norwegian defense spending next year by 4 percent above inflation, the largest rise in NATO outside the United States, and to speed up arrangements for U.S. warplanes and Marine reinforcements to be rushed here to help defend NATO's northern flank if it were attacked.

Government officials and politicians of both Conservative and Labor parties interviewed here said the Labor government of former prime minister Gro Harlem Brundtland might have taken some of the same steps had it not been defeated in September's national election.

The sources blamed Norway's widely publicized disagreements with the United States, which contrasted with traditional Labor government support for NATO, on pressure from the anti-NATO left wing within Labor and from the country's nuclear disarmament movement.

The sources cautioned that a significant minority of Norwegian politicians and citizens remain skeptical about the United States and the North Atlantic Treaty Organization.

For the moment, they said, the voices of skepticism have been muted by President Reagan's "zero-option" proposal for reducing theater nuclear weapons in Europe and by the incursion of a Soviet submarine believed to be carrying nuclear weapons into the territorial waters of neighboring Sweden.

"There has been a change from a year or even two months ago," said Defense Minister Anders Sjaastad. "The yardstick for the future will be the progress that is made in the theater nuclear weapons negotiation. I have tried to tell the public that it will be a long, hard negotiation."

The new face of Norwegian foreign policy under the Conservatives was shown in Washington last month when Norwegian Foreign Minister Svenn Stray, smiling broadly after meetings with Secretary of State Alexander M. Haig Jr. and Defense Secretary Casper Weinberger, emphasized their complete accord on all issues.

Stray and Sjaastad attributed the absence of disagreement in part to the Reagan administration's adopting the zero-option approach in the nuclear arms talks in response to pressure from Norway and other European allies.

Former prime minister Brundtland warned against Washington counting excessively on the Conservatives. "I don't believe what the United States needs in Norwegian foreign policy is a smiling foreign minister," she said.

She said the Labor Party was divided about attitudes toward the United States and NATO, but she claimed that once a policy decision had been reached by the party, still Norway's largest, "it could assemble a consensus from the entire Norwegian population."

"It would be a mistake for the Americans to assume that a Conservative government in Norway was like the Reagan administration," said a senior Western diplomat, who forecast potential disagreements between Oslo and Washington over Reagan's policy in Latin America and other Third World issues.

He also noted that Willoch's minority government depends on support in parliament from centrist parties containing pacifist minorities such as Labor's left wing.

"This government recognizes legitimate fears here about the possibility of nuclear war in Europe," said Defense Secretary Sjaastad, "yet we are standing fast on defense."

The Willoch government is increasing military spending beyond NATO's target of 3 percent above inflation annually both to strengthen Norway's own defenses and to hasten arrangements for U.S. reinforcements in wartime.

Under a recent agreement with the United States, weapons and equipment will be stored and airfields readied in northern Norway, several hundred miles from the Soviet border, so that an extra brigade of Norwegian troops could move there in a crisis. Other facilities are being readied in central Norway to store weapons and equipment for U.S. Marine reinforcements who could be rushed north later if necessary.

Norwegian defense officials said their job had been made easier by the Soviet submarine that penetrated Sweden's coastal defenses before running aground a month ago.

"It woke up a lot of people who had been dreaming," said a senior Norwegian general, who added that mysterious submarines have frequently been spotted but never caught along Norway's long coastline. Norwegian surveillance of Soviet submarines is important for the defense of allied supply lines across the North Atlantic.

Stray said Norway's new government would move cautiously in contacts with its Soviet neighbor, leaving discussion of questions such as that of a Nordic nuclear-free zone to U.S. negotiations with the Soviets on behalf of NATO. The top priority in scheduled diplomatic discussions between the Norwegians and Soviets this month in Moscow and Oslo is a long-standing dispute over economic rights in overlapping territorial waters in the Barents Sea.

Norwegian-Soviet relations, however, could be complicated by recent newspaper reports in Oslo that three senior Soviet diplomats were under investigation here for offering Norwegians money to write letters to newspapers calling for a Nordic nuclear-free zone.

The Norwegian Justice Ministry said in a formal statement that it has no evidence to substantiate the allegations. The Soviet Embassy here denied the allegations.