NEW YORK CITY, Jan. 29 -- The student leaders who will meet with Secretary of State Dean Rusk Tuesday have written two more letters -- one to Rusk and another to President Johnson -- sharpening their questions about the Administration policy in Vietnam.

Their letter to Johnson, according to Steven Cohen of Amherst, one of the drafters, "discerns contradictions between what the Administration says and what it does."

The one to Rusk, which will arrive at the State Department barely 24 hours before their meeting, defines more clearly the doubts which the student leaders discussed in their first letter to Johnson, Dec. 30. In that letter, the student-body presidents and newspaper editors reported that increasing numbers of students across the country doubted that U.S. interest in Vietnam were sufficiently vital to justify our growing commitment there.

Invitation From Rusk

Although they have not yet heard from the President, they received a response from Rusk Jan. 4 and an invitation to the State Department.

They declined to comment any further today on the substance of the letters, or to reveal how many of the leaders have signed it. Working past midnight tonight on the final wording, they planned to deliver the letters tomorrow morning and then release them at a press conference at 3 p.m.

Asked why they had waited until now to write Rusk, a spokesman for the students said that problems "of logistics"-- conflicting exam schedules and long distances -- had prevented them from gathering earlier.

One of the "minor strategic considerations," a spokesman said, was the possibility of attracting national attention to the meeting with Rusk.

They considered releasing the letters exclusively to the New York Times, as they did with their first letter to the President. But they did not finish the letters in time for the paper's Monday edition and decided that it would be fairer in any case to release the letters to all the newspapers at a press conference.

Their main objective in writing to Rusk, the spokesman said, was to "pinpoint the areas of discussion," and "carry the dialogue one step further."

State Department officials, informed Thursday of the students' plan to write another letter, had said that this move would be "playing unfair" and that it wouldn't "go over very well" with the Secretary.

But, after talking to students over the weekend, the same official said today that they had "cleared up misunderstandings," and that the students had a "right to do anything they want."

Asked by a reporter about the second Johnson letter, the official said that the students had not told him about it. He declined comment.

The letters were drafted by a 16-member executive committee, which began meeting in small groups yesterday afternoon at Dumbarton College in Washington and continued past 5 a.m. this morning.

The group included Gregory G. Craig '67, chairman of the Harvard Undergraduate Council and one of the organizers of the student leaders, as well as representatives from Michigan State University, Vassar College, the University of Buffalo, and the University of North Carolina