Senate Majority Leader Robert C. Byrd (D-W.Va.) called on President Carter yesterday to accept the challenge of a face-to-face debate with his rival for the Democratic presidential nomination, Sen. Edward M. Kennedy (D-Mass.).

Byrd said such a debate would "promote unity in the party and sharpen the issues" for the benefit not only of the listening public but for the candidates. "It could be beneficial to both candidates," he said.

Byrd coupled this adoption of a position long held by Kennedy with a warning that Carter may not have the nomination sewn up. "Events can change drastically," he said. "Nobody can say today what the situation is going to be at the convention based solely upon the arithmetic of the delegate count at this point.

He noted, however, that if one candidate were to consider dropping out of the race, the period just after the June 3 primaries in California, New Jersey, and five other states "would be an appropriate point for one to consider the wisdom of going on." Carter has lost to Kennedy in the large industrial states of Michigan, New York, Pennsylvania and Massachusetts and the "big three" June primaries are seen as a key test for both men. Carter leads in delegates.

Asked at his regular news conference what issues Carter needed to sharpen, Byrd replied, "Well, there's the domestic issues and then there are the foreign issues." He added, however, that the debate could help remind the public of Carter's "many pluses," which Byrd said included the Panama Canal treaties, the Camp David Israeli-Egyptian accords, arms sales in the Middle East and efforts to strengthen NATO.

Kennedy's pluses include "the service of raising economic issues, things that ought to be discussed," Byrd continued. Carter would not be admitting any weakness in agreeing to debate, Byrd insisted, since the presidential race is unique. "There's no difference debating in the primary and in the general election," he said.

Democratic prospects in the November election are good, Byrd said, since Republican front-runner Ronald Reagan's "simplistic, patent-medicine answers . . . will create a public relations nightmare in which he may repeatedly shoot himself in the foot."

Turning to other matters, Byrd said it would have been well for Carter to attend the funeral service of President Tito of Yugoslavia, which drew dozens of other world leaders. However, the important thing is that Yugoslavians recognize the U.S. commitment to their independence and continued nonalignment, Byrd said. "We've made that clear and there should not be any doubt about it," he said.

Byrd reported that the fiscal 1981 budget is moving along in Congress and said he hoped to conclude Senate work on it Monday and House-Senate conference efforts by Thursday of this week.