HONOLULU — The Obama administration has decided in principle to allow the embattled president of Yemen, Ali Abdullah Saleh, to enter the United States for medical treatment, subject to certain assurances, two administration officials said Monday.

But those conditions — including a proposed itinerary — have not yet been submitted to the American Embassy in Yemen, these officials said, and no visa has yet been issued to Mr. Saleh.

The decision of whether to admit Yemen’s longtime leader has stirred a vigorous debate within the administration, with some officials fearing sharp criticism for appearing to provide a safe haven for a reviled Arab figure accused of responsibility for the death of hundreds of antigovernment protesters.

The complex negotiations over Mr. Saleh’s visa request attest to the high stakes for the administration, which urgently wants to secure room for political progress in Yemen but does not want to allow Mr. Saleh to use a medical visit as a way to shore up his political position. Nor do they want to play into Mr. Saleh’s penchant for keeping people off kilter.