Washington (CNN) - Attacks on U.S. diplomatic posts in Libya and Cairo sparked a sharp exchange of political attacks Wednesday, as Mitt Romney accused President Barack Obama's administration of sending "mixed signals" on American values, and Obama painted his rival as crudely inserting politics where they don't belong.
"I think President Obama has demonstrated a lack of clarity as to a foreign policy," Romney said in Jacksonville, Florida, continuing a line of criticism his campaign began late Tuesday, when it issued a statement that labeled the U.S. response to attacks on the American embassy in Cairo as "disgraceful."
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Obama, along with other Democrats, pushed back, saying Romney was injecting politics during a time of still-developing international crisis. Like Romney, the president did not mince words about his political opponent.
"Gov. 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 during an interview with CBS. "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."
Romney's first statement came Tuesday night around 10 p.m. ET, as reports indicated an American diplomatic worker in Benghazi, Libya, had been killed in an attack on the consulate there. The Republican candidate's statement was sent before news broke that the American ambassador to Libya, J. Christopher Stevens, had been killed in the attack.
In separate protests in Cairo, several men scaled the walls of the U.S. embassy and tore down its American flag. The violence in both Libya and Egypt stemmed from anger about an online film considered offensive to Islam.
In his statement, Romney said he was "outraged" by the attacks in Benghazi and Cairo, but took harsh aim at the Obama administration for what he characterized as a weak response to the violence.
"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," Romney wrote, an apparent reference to a statement from the U.S. Embassy in Cairo that denounced the anti-Islam film that is the source of the protesters' anger. The embassy's statement was released before protesters stormed the American embassy in Cairo on Tuesday.
MORE: Romney's political pretzel over Libya
The embassy in Egypt wrote 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."
"Respect for religious beliefs is a cornerstone of American democracy," the statement continued. "We firmly reject the actions by those who abuse the universal right of free speech to hurt the religious beliefs of others."
A second statement, from U.S. Secretary of State Hillary Clinton, said anger over the film did not justify the violence.
"The United States deplores any intentional effort to denigrate the religious beliefs of others," Clinton wrote. "Our commitment to religious tolerance goes back to the very beginning of our nation. But let me be clear: There is never any justification for violent acts of this kind."
Obama's presidential campaign responded quickly to Romney's statement, saying their rival was using events in the Middle East for blind political gain.
"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," Obama campaign press secretary Ben LaBolt wrote.
In his remarks Wednesday in Florida, Romney said it was "never too early for the United States government to condemn attacks on Americans and to defend our values."
"I think it is a terrible course for America to stand in apology for our values," Romney said. "That instead when our grounds are being attacked and being breached that the first response of the United States must be outrage at the breach of the sovereignty of our nation. And apology for America's values is never the right course."
The fact that the statement came from the American embassy in Egypt, and not from the president himself, doesn't negate Obama's responsibility, Romney said.
"Their administration spoke. The president takes responsibility not just for the words that come from his mouth but also from his ambassadors, from his administration, from his embassies, from his State Department," the Republican candidate said.
Newt Gingrich, the former House speaker and a surrogate for Romney, also said the Republican's statement was justified.
"Governor Romney's statement is pretty clear," Gingrich said on CNN's "Starting Point." "If Gov. Romney were president he would be enraged at the Egyptians for tolerating the attack on the embassy. Both countries have an obligation to protect our embassies."
Other Democrats quickly chastised Romney Wednesday, saying the Republican was callously inserting politics in a developing story. Sen. John Kerry of Massachusetts, the chairman of the Senate Foreign Relations Committee, called Romney's remarks "about as inappropriate as anything I've ever seen at this kind of a moment."
"They are flat wrong," Kerry said. "They demonstrate an insensitivity and a lack of judgment about what is happening now. To make those kinds of statements before you even know the facts, before families have even been notified, before things have played out, is really not just inexperienced, it's irresponsible, it's callous, it's reckless. And I think he ought to apologize and I don't think he knows what he's talking about frankly. It's that simple."
"I'm sorry the decision was made in the Romney campaign to make this a political issue. It is not," U.S. Sen. Dick Durbin (D-Illinois) said. "It is a tragic human issue and we should be together as a nation condemning this terrible violence against our ambassador and those who worked in the Libyan embassy."
A second diplomatic flashpoint – the White House's reported refusal to grant a meeting between Israeli Prime Minister Benjamin Netanyahu and Obama – also seemed poised to break into the presidential campaign Wednesday.
CNN's Wolf Blitzer, citing Israeli sources, reported that the Israelis were told Obama's schedule would not permit a meeting even though Israel offered to have Netanyahu travel to Washington.
Obama and Netanyahu are both due to address the United Nations in New York in late September but not at the same time.
The Obama administration pushed back later Tuesday.
"Contrary to reports in the press, there was never a request for Prime Minister Netanyahu to meet with President Obama in Washington, nor was a request for a meeting ever denied," the White House said Tuesday night in its statement, which made reference to "our close cooperation on Iran and other security issues."
Wednesday's detour to foreign policy comes after months of a near-singular campaign focus on jobs and the economy. Romney makes little mention of foreign policy on the stump, and was criticized for not mentioning Afghanistan during his speech at August's Republican National Convention.
The last time foreign policy was in the spotlight during the 2012 presidential campaign came in late July, when Romney traveled to England, Israel and Poland to meet with leaders and tour historic sights. Despite a few successes on the trip, including being endorsed by a beloved Polish labor leader, the foreign swing is remembered chiefly for a series of gaffes from the GOP candidate, including suggesting that London was not well-prepared for the Summer Olympics.
Voters consistently say in polls that Obama would better handle America's relationships with other countries if re-elected. In the latest CNN/ORC International survey released earlier this week, President Barack Obama had a 54%-42% advantage over Romney on foreign policy.
CNN's Ted Barrett and Paul Courson contributed to this report.