Chancellor Helmut Schmidt left today for a four-day visit to the United States intent on dispelling concern in Washington about West Germany's restrained plans for defense spending next year.

In a barrage of recent public statements, Schmidt has sought to repair new strains in U.S.-West German relations brought on by the initial plan of his reelected coalition government to raise defense spending next year by only 1.8 percent.

This is considerably short of the target set in 1978 by NATO members to raise defense spending by a real 3 percent annually until 1986, and well below the 5 percent-plus increase being considered by President-elect Ronald Reagan.

Schmidt now says his government will meet its 3 percent NATO pledge, although it will have to be done by supplementing the 1981 Bonn budget.

The chancellor, who arrived in New York tonight, is scheduled to meet with President Carter on Thursday after spending Wednesday in New York. He is also due to see several top Reagan aides, although no meeting with Reagan was formally requested, in deference to Reagan's announced intention not to see foreign leaders yet.

In recent summit meetings with French President Valery Giscard d'Estaing and British Prime Minister Margaret Thatcher, Schmidt has joined in welcoming the Reagan election. The chancellor, who had been critical of Carter's lack of consultation with European leaders, has said he looks forward to more intensive consultation with a Reagan administration and, at the same time, made special note of Reagan's "intended renewal of American leadership."

But Bonn's decision to cut corners, at least initially, on defense spending hardly seems the best way to start off with a new Republican administration.

U.S. officials have attacked Bonn's projected defense budget as undermining the resolve of the Western alliance to finance needed modernization. Western defense planners worry that if West Germany, which has Europe's strongest conventional army, gives ground on the 3 percent target, there will be little chance of retrieving the already compromised commitments of smaller NATO members such as Denmark, Belgium and the Netherlands.

Schmidt has appeared irritated by the controversy, viewing it as an annoying echo of what happened last year, when Bonn similarly announced an increase of less than 3 percent in defense spending but managed, through two supplementals this year, to bring the total up to 2.8 percent.

The official rationale for Bonn's own initially low defense spending figure is the projected poor performance of the West German economy -- a zero-growth rate is widely forecasted for 1981 -- and the political unattractiveness of deep cuts in social welfare and farming benefits.

Immediately after Schmidt's reelection in October, his aides put out word that the world should not expect as much financial assistance from a wealthy Bonn as in the past. "We are not a hen that can lay golden eggs," the chancellor said Sunday in a West German television interview.

Bonn's own stubbornness on defense spending may itself prove an important bargaining lever against a cost-conscious Washington. By begrudgingly conceding to meet its NATO commitment, some Bonn officials hope to persuade Washington to back off from a request list for further costly West German support of American troops stationed here. The list was formally submitted to the Bonn government earlier this month.

During his visit, Schmidt can be expected to argue that it is not how much but rather how defense money is spent, and on this score, West German troops compare favorably with other NATO forces. Moreover, Bonn has averaged yearly increases in defense spending of 2.7 percent during the past decade while the American defense effort slacked during some of that post-Vietnam period.

Additionally, the expensive support Bonn gives to West Berlin and the land ceded to U.S. and other allied forces stationed in Germany are not counted in Bonn's NATO commitment while the funds West Germany gives to bolster Turkey and Greece on the alliance's southeastern flank are included.

Then, too -- as Schmidt has often noted in the past when under U.S. attack -- West Germany still has a draft and can call up 700,000 reserve forces in short time. The chancellor has suggested that America return to general conscription.

Even so, the 3 percent spending target has taken on a symbolic significance for Washington as a measure of Bonn's steadfastness in the alliance. Schmidt's mission this week is not as delicate as the one last March in which he had to win understanding for Europe's sustained interest in detente following the Soviet invasion of Afghanistan. But the chancellor nonetheless finds himself on the defensive once again.