OBOCK, Djibouti — Saudi Arabia said Tuesday that it was halting a nearly month-old bombing campaign against a rebel group in neighboring Yemen that has touched off a devastating humanitarian crisis and threatened to ignite a broader regional conflict.

The announcement followed what American officials said was pressure applied by the Obama administration for the Saudis and other Sunni Arab nations to end the airstrikes. The bombing campaign, which has received logistical and intelligence support from the United States, has drawn intense criticism for causing civilian deaths and for appearing to be detached from a broad military strategy.

A Saudi Defense Ministry statement quoted by the country’s news agencies said that the campaign, called Operation Decisive Storm, had achieved its objectives. But it was unclear exactly how much the airstrikes had advanced Saudi Arabia’s stated goal of helping restore a Yemeni government that collapsed many weeks ago as Houthi rebels took over the country’s capital, Sana. Analysts said the announcement could possibly clear the way for a different type of military intervention.

Weeks of fighting in Yemen, which was already suffering from the absence of any central authority, have left nearly a thousand people dead and provided an opening for Al Qaeda’s branch there to expand its territory. The conflict further threatened to entangle the United States and Iran in a potential military confrontation, just as they are about to continue difficult and delicate negotiations that they hope will result in a final nuclear agreement by the end of June.