Updated

Mitt Romney on Wednesday stood by his criticism of the Obama administration for its early response to the attack on the U.S. Embassy in Cairo, even as he and President Obama mourned the murder of four Americans including the U.S. ambassador in a separate attack on the U.S. Consulate in Benghazi, Libya.

Romney said the administration's initial response to the attack in Cairo was "akin to apology" and a "severe miscalculation."

Obama retorted in an interview with CBS News that his rival "seems to have a tendency to shoot first and aim later."

Said Obama: "It's important for you to make sure that the statements that you make are backed up by the facts."

Both overseas assaults were purportedly linked to a video being promoted in the U.S. that ridiculed Islam's Prophet Muhammad. The U.S. Embassy in Cairo at first issued a statement saying, in part, that it condemns "the continuing efforts by misguided individuals to hurt the religious feelings of Muslims -- as we condemn efforts to offend believers of all religions."

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The Romney campaign issued a statement overnight calling that response "disgraceful," prompting criticism from the president's campaign. The Obama campaign accused Romney of launching a "political attack" as reports were first surfacing that one American had been killed. By Wednesday morning, the death count was at four.

Romney, as he condemned the "outrageous" Libya attack during a stop Wednesday in Jacksonville, Fla., did not back down from his criticism of Obama.

"I think it's a terrible course for America to (issue) an apology for our values," Romney said. "An apology for America's values is never the right course."

The Obama administration reportedly disavowed the Cairo Embassy statement, but Romney said Wednesday that "the embassy is the administration."

He said the disavowal "reflects the mixed signals they're sending in the world."

Romney went on to critique Obama's overall foreign policy, calling it a "hit-or-miss approach." Romney and his surrogates have been stressing foreign policy after the president, in his nomination address last week in Charlotte, called Romney and running mate Paul Ryan "new" to the issue.

The Associated Press contributed to this report.