“It’s disgraceful that the Obama administration’s first response was not to condemn attacks on our diplomatic missions, but to sympathize with those who waged the attacks,” said the statement, issued about 10:30 p.m.

But by Wednesday morning, as the sequence of events and the scope of the tragedy in Benghazi became more clear, Mr. Romney’s initial statement and ensuing comments were coming under attack as clumsy at best. By later in the day, even some Republican allies were declining to follow his lead, and some acknowledged that he looked as if he was trying to score points in the middle of a crisis.

For a country looking to understand how Mr. Romney, a Republican candidate with no foreign policy experience, would respond to a major crisis, this was a first glimpse. And as an adviser to the campaign who worked in the George W. Bush administration said on Wednesday, Mr. Romney’s accusation that Mr. Obama had invited the attacks because he had weakened America looked like “he had forgotten the first rule in a crisis: don’t start talking before you understand what’s happening.”