The United States and Japan have agreed to hold further discussions during the next few weeks in hopes of resolving the problem of Japanese auto imports after making no apparent progress toward voluntary import restrictions during high-level talks this week.

The agreement to hold further talks both here and in Tokyo followed a meeting between Japanese Foreign Minister Masayoshi Ito and President Reagan, who had requested the upcoming discussions, according to Foreign Ministry spokesman Taizo Watanabe. The Japanese first want to see what the administration plans to do to help its own industry and what Reagan's economic recovery program will do, Watanabe said. He added that the major consideration was maintaining free trade.

Meanwhile, General Motors Corp. yesterday gave its best 10-day sales report in four years. Its mid-March domestic auto sales were their second highest in history for that period, and were 29 percent above last year's.

Ford Motor Co. auto sales were down 8.1 percent for the period while Chrysler sales were up 18.1 percent in mid-March. American Motors Corp. sales declined 32 percent from last year.

The Big Three automakers offered direct cash rebates during the period.

Japanese and American officials were careful to label the upcoming talks as "discussions" and not "negotiations." What we have not now is an expression or wish on the part of the [Reagan] administration to have some talks by both sides," Watanabe said. "Anyway, we are ready to discuss."

Watanabe said Reagan made no other requests of the Japanese. "We simply agreed to have continued discussions, and out of the discussions some conclusions may be reached," but nothing had been said about a voluntary import-restraint agreement between the U.S. and Japan. "We agreed to conduct discussions. The result of the discussions are not yet known," he said.

The areas to be discussed are "the extent of the public opinion situation in both countries, what the United States plans to do domestically in response to the situation and the legal considerations which exist on both sides," according to a statement from Ito read by Watanabe at a press briefing. "A major objective would be to preserve the principle of free trade."

The agreement for further discussion puts off for awhile any decision by Reagan on import restraints -- voluntary or otherwise. White House sources said the talks between Ito and Reagan hadn't gone particularly well. One sign was that the deadline set last Friday by Chief of State James A. Baker for the administration's decision on the issue seemed to be slipping. White House Press Secretary James S. Brady refused to say that there is any deadline.

Ito told reporters at a luncheon that it would be hard for him to issue orders to his companies to restrict their exports to the United States because the International Trade Commission last year 3 to 2 that imported cars weren't the major cause of Detroit's problems and because Reagan's own Cabinet is publicly split on the issue.

A high-level administration source said that pressure from Congress for import limits was not unwelcome at this point because it could be used as leverage against the Japanese. Ito told reporters during a luncheon yesterday that Reagan told him it would be difficult for him to veto import quota legislation because of the rising tide of protectionism here.

Congressional pressure was evident in two visits to the White House yesterday. Sen. John C. Danforth (R-Mo.) told the president he remained serious about his legislative efforts to restrict for three years Japanese imports to 1.6 million, 300,000 less than the number sold last year.

Senate Majority Leader Howard Baker (R-Tenn.) told reporters after his meeting with Reagan: "I think the president must surely understand that there's a building pressure in the Congress to do something by statute if the Japanese don't do something voluntarily. . . I don't want that, but that's going to happen if the Japanese don't understand that the situation out of hand."