RIYADH, Saudi Arabia — The uncertainty surrounding the political future of Yemen’s president, Ali Abdullah Saleh, deepened Tuesday as he was treated for far more severe burns than had first been disclosed, while maneuvering intensified in the capitals of Yemen, the United States and Saudi Arabia to head off an emerging and dangerous power vacuum.

Mr. Saleh’s sudden departure from Yemen initially prompted warring factions to call a cease-fire, but that failed to stabilize the badly fractured nation as fighting on Tuesday intensified in the south between militants and the government, leaving dozens dead.

While mediators move toward establishing a transitional government, Mr. Saleh’s condition — and his prospects for recovery — emerged as the crucial factor in determining who will rule the nation, which is an important ally of the United States in fighting terrorism. While Washington and Riyadh have wanted Mr. Saleh to step down in the face of months of protests and increasing violence, there was no agreement Tuesday on how to proceed while he is in the hospital here.

Interpretations of Mr. Saleh’s medical state have varied according to the competing demands of the camps that would like different outcomes in Yemen.