Washington — Having held together through a difficult challenge, the United States and its European partners have entered a new period of debate over the state of the Atlantic alliance.
The debate on both sides of the Atlantic ranges from old questions about economics and defense spending to new questions about military strategy. As US Assistant Secretary of State Richard R. Burt put it earlier this week in a congressional hearing, ''I think we're in a period where a hundred flowers are blooming about the alliance.''
While Mr. Burt called this a healthy development within what he described as a strengthened alliance, critics of the Reagan administration refer to the debate as one more sign of what they call deepening differences. But according to Burt, the current transatlantic arguments are healthy because debate is the ''prerequisite of intelligent change, and the alliance must adjust if it is to be effective.'' Such debate is natural, he adds, because debates have taken place regularly throughout NATO's nearly 35 years.
At the White House, meanwhile, President Reagan greeted France's President Francois Mitterrand Thursday in what amounted to a celebration of unifying factors in the Atlantic partnership. Despite the philosophical differences between the French socialist and Reagan, the two leaders appear to get along well. Relations between the US and France have rarely seemed stronger. President Mitterrand vigorously supported the deployment of new American missiles in Europe, which began at the end of last year as part of an effort to counter growing Soviet missile strength.
During White House welcoming ceremonies, Mitterrand said France remains ''a constant ally that can be counted on.''
But it also seems clear that issues that were suppressed while the Atlantic partners faced a strong challenge both from the Soviet Union and from European demonstrators over the deployment of the new missiles have now surfaced. The lines of debate were most dramatically drawn by former Secretary of State Henry Kissinger, who, in an essay published by Time magazine earlier this month, suggested that the present controversies within NATO are ''both unprecedented and unsettling.''
Dr. Kissinger listed four problems in particular which he said were gnawing at the alliance: (1) lack of an agreed, credible strategy; (2) continued European opposition to the deployment of new US missiles; (3) a dispute over the alliance's posture toward the Soviet Union; (4) a European view of US approaches to the third world as ''hopelessly tainted by an obsession with Soviet ambitions.''
Lawrence Eagleburger, the US undersecretary of state for political affairs, also stirred controversy earlier this year when he warned at a seminar that the US might have to turn away from Europe and toward the Pacific Basin countries. But many specialists in the Reagan administration have since contended that both Kissinger and Mr. Eagleburger overstated alliance differences.
Administration officials have argued with Kissinger's recommendation that a European military officer take the traditionally American position of supreme allied commander in Europe. Assistant Secretary Burt, in his congressional testimony this week, contended that to have an American in this position is ''a very visible symbol of the US commitment'' to the defense of Western Europe.
Kissinger had suggested that if Western European nations refuse to accept greater responsibility for their ground defense, the US should withdraw up to half of its troops from Europe. Burt argued that such a move would have a ''demoralizing'' impact on the alliance.
But a number of US congressmen agree with Kissinger's complaint that the West Europeans are not doing enough for their own defense. On Tuesday, Rep. Don J. Pease, a Democrat from Ohio, told the House subcommittee on Europe and the Middle East that he thought the Reagan administration was ''allowing our allies to neglect their fair share of the common defense burden.'' The Ohio congressman said nine nations in the 15-member NATO alliance had failed to achieve a promised 3 percent real increase in defense spending.
Representative Pease has introduced a resolution calling on all the NATO nations, as well as Japan, to meet or exceed their pledges to increase defense spending. He said that in their relations with Europe, Americans were acting ''too much like a patsy.''
One Capitol Hill specialist on such matters says there is considerable support for Pease's view that defense ''burden sharing'' could again become a major issue by the end of the year.
But it is in economic and trade relations that Assistant Secretary Burt and some other specialists have been predicting potential trouble for the US and Europe. In a statement made some weeks ago, Burt cited a comment from German Foreign Minister Hans Dietrich Genscher, who has said that having met the challenge of the new missile deployment, Germany must now face up to a second great challenge - that of economic and technological change. This challenge, said Burt, is posed in the most immediate way by growing pressure for protectionism. He complained that Western Europe had begun to take export markets away from the United States, using subsidies to undercut American prices.