Behind the scenes, the officials, who spoke on the condition that they not be named because they were discussing internal deliberations, said Mrs. Clinton had been advocating the stronger U.S. response, but the president resisted. When he finally took her advice, the aides said, he did so without informing her first.

This was the first known example of awkwardness between the two former rivals for the Democratic nomination for president since they made up following Mr. Obama's election. The disagreement also gave some insight into the Obama administration's foreign policy decision-making process five months into its term.