SANA, Yemen — Yemen on Sunday appeared to reject a cease-fire offer from the leader of the Houthi rebels, raising fresh questions about a festering conflict that has diluted the government’s ability to deal with a growing insurgency by Al Qaeda.

The leader of the rebels, Abdul-Malik al-Houthi, issued a statement on Saturday accepting the government’s terms for a cease-fire. But on Sunday, Yemen’s National Defense Council said it would cease military operations only after the rebels had complied with those terms, which include disarming, releasing captured soldiers and property, removing roadblocks and withdrawing from strategic positions.

Another condition was that the rebels cease all attacks on Saudi Arabia, which lies just across the border from the rebels’ terrain in northwestern Yemen, and vow not to attack it again. Last week Mr. Houthi declared a unilateral cease-fire with Saudi Arabia, but Saudi officials have rejected that offer, insisting that the rebels withdraw from the border.

Yemeni officials have said the continuing war has drawn resources away from the struggle with Al Qaeda. The terrorist group’s Yemen-based branch has drawn international attention since it claimed credit for the Dec. 25 attempt to bomb a jetliner as it was approaching Detroit.

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