WASHINGTON — Saudi Arabia’s resumption of airstrikes against Houthi rebels in Yemen on Wednesday, only hours after it abruptly declared a halt to most military operations, reflected the difficulty of finding a political solution to the crisis. It also showed the challenges facing the Obama administration as it increasingly relies on allies in the Middle East.

Senior Saudi officials made clear on Wednesday that they had not formally declared an end to bombing. Rather, the Saudi ambassador to the United States, Adel al-Jubeir, said the campaign was shifting to a new phase — one in which Saudi airstrikes would be more limited and come only in response to Houthi attacks, such as the assault against Yemeni troops in Taiz.

“The decision to calm matters now rests with them,” Mr. Jubeir told reporters at the Saudi Embassy here. He asserted that Saudi Arabia was curtailing its nearly monthlong strategic air campaign because it had ostensibly destroyed Houthi missiles, heavy weapons and aircraft that posed a threat to Saudi Arabia and the region.

The ambassador did not mention the intensifying international pressure, including from the Obama administration, to stop airstrikes that medical and relief organizations said were killing hundreds of civilians, and to lift an embargo on food, fuel, water and medicines that was contributing to a growing humanitarian catastrophe. But American officials and Middle Eastern diplomats privately acknowledged that this was clearly a factor in the Saudi calculation.