(CNN) - Asked in an interview on Thursday, Mitt Romney declined to continue a terse exchange between himself and President Barack Obama. In the latest volley, the president asserted that his Republican challenger had not "thought through the ramifications" before issuing a statement sharply critical of Obama on Tuesday over the latest unrest in the Arab world.
"Governor Romney seems to have a tendency to shoot first and aim later, and as president, one of the things I've learned is you can't do that," Obama said Wednesday in an interview with CBS News. "It's important for you to make sure that the statements that you make are backed up by the facts and that you've thought through the ramifications before you make them."
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In his own interview with ABC News a day later, Romney declined to take an opportunity to hit Obama in return.
"No direct response when the president said you 'shoot first and aim later?' " Romney was asked.
"Well, this is politics," the candidate replied in one excerpt released by the news outlet. "I'm not going to worry about the campaign."
Obama was speaking of Romney's sharp criticism over the Obama Administration's response to attacks on U.S. posts in Libya and Egypt, including the killing of several Americans.
"I'm outraged by the attacks on American diplomatic missions in Libya and Egypt and by the death of an American consulate worker in Benghazi," Romney said in a late Tuesday statement. "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."
The next day, Romney hit Obama for having "demonstrated a lack of clarity as to a foreign policy."
Romney's allegation that administration expressed sympathy appeared to refer to a statement and tweets from the U.S. embassy in Cairo. The statement said the embassy "condemns the continuing efforts by misguided individuals to hurt the religious feelings of Muslims – as we condemn efforts to offend believers of all religions... Respect for religious beliefs is a cornerstone of American democracy. We firmly reject the actions by those who abuse the universal right of free speech to hurt the religious beliefs of others."
His Tuesday night statement came as news broke that a consulate employee had been killed in an attack on the U.S. consulate in Benghazi, but before it was known that one of four Americans to the American was the ambassador to Libya.
Obama campaign press secretary Ben LaBolt followed Romney's late Tuesday statement with one which read, "We are shocked that, at a time when the United States of America is confronting the tragic death of one of our diplomatic officers in Libya, Governor Romney would choose to launch a political attack."
And Obama went on offense in a Wednesday interview, accusing Romney of "a tendency to shoot first and aim later."
Also in the Thursday interview with ABC News, Romney reacted to the Federal Reserve's Thursday decision to implement a third round of economic stimulus known as quantitative easing, or QE3.
"What Bernanke is doing is saying that what the president is saying is wrong," Romney said of Federal Reserve chief Ben Bernanke in the interview. "The president is saying the economy is making progress, coming back. Bernanke is saying no, it's not."
Romney's statement in the interview was in line with what he has said previously on the subject of another round of quantitative easing.
"I think the Fed's first action - quantitative easing - was effective to a certain degree," he told CNN Chief Political Analyst Gloria Borger in August. "But I don't believe the QE2 - second quantitative easing had the impact they were looking for."
"I am sure the fed is watching and will try to encourage the economy," he said. "But I don't think a massive new QE3 will help this economy."
– CNN's Gregory Wallace, Ashley Killouth, Kevin Liptak, and Kevin Bohn contributed to this report