More than 250 student leaders from across the country came to the White House yesterday for what turned into a soft-sell sales pitch from President Carter for his draft registration proposal -- and for his political future as well.

Speaking to the group in the East Room after a day of briefings by White House aides on domestic and foreign issues, Carter defended his proposal to reinstitute registration for the draft as an "important symbolic act."

But at the same time he made a conciliatory gesture toward the Soviet Union, saying in remarks both to the students and to out-of-town newspaper editors earlier in the day that he remained committed to "detente" with the Soviet Union.

Among the achievements he wanted to leave behind, he told the students, was a "firm, sound friendship and detente between ourselves and the Soviet Union."

To the editors, he said: "We are committed to the preservation of detente. Once Soviet troops are withdrawn from Afghanistan and the threat of military action by them is removed, then we'll be very glad to proceed aggressively again on further progress toward the control of weapons and strengthening of our ties with all nations . . ."

Carter's defense of his draft registration proposal drew at least as much applause as a student's assertion of opposition to it. And Carter drew strong applause when he asked for students' appreciation for the "difficult decisions" he's had to make and asserted, "I don't know of any actions that I've taken that caused our nation embarrassment."

Although White House aides said the session had been planned for months and denied it was prompted by signs of student concern over draft registration, many students came expecting a registration pep-talk. Several noted with wry amusement that the national security affairs adviser, Zbigniew Brzezinski, had to bring up the subject himself in his discussion with the students after none of them broached it directly.

They also say the event as a political one. They roared with laughter when a reporter asked if they thought the meeting had political overtones. "We're not dumb," said one.

Several students also came away from their White House visit with invitations to a campaign breakfast this morning for Sen. Edward M. Kennedy (D-Mass.), the president's chief rival for the Democratic presidential nomination this year. They said someone was handing them out as they entered the White House gate yesterday morning.

The closest thing to a confrontation was a polite but firm statement of opposition to the draft and to any American military involvement in the Third World by Russ Bellant student body president at Wayne State University in Detroit.

Carter took it in good humor, and Bellant said afterward that his own views, judging by the applause were probably in a minority at the meeting. Bellant said he thought Carter would lose votes because of his registration proposal but doubted that it alone would cost him reelection.

In response to questions about U.S. strategy for the Persian Gulf, he suggested a mutual defense pact among Moslem nations. "I would like to see the Moslem countries, for instance, pledge themselves that if any of their brother nations are invaded by the Soviet Union that they would respond jointly to that threat," he said.

But he added that the United States must also demonstrate that it is "marsheled if necessary to respond" and said draft registration would symbolize this resolve.