Romney also angered Palestinian leaders with a reference to cultural differences as a reason for differing levels of prosperity between Israel and the Palestinian territories.
In addition, a secretly recorded video of a private campaign event in May showed Romney casting doubt on the possibility of reaching a two-state solution in the Middle East with independent Israeli and Palestinian states.
On Monday, Romney pledged to recommit his administration to seeking the two-state solution and blamed Obama for what he called a negotiation process that has "devolved into a series of heated disputes at the United Nations."
"In this old conflict, as in every challenge we face in the Middle East, only a new president will bring the chance to begin anew," Romney said.
"I know the president hopes for a safer, freer, and a more prosperous Middle East allied with the United States. I share this hope," he said."But hope is not a strategy."
Romney also has faced negative headlines over his quick response to the Benghazi consulate attack. Soon after word broke of the violence, he fired off a statement that was criticized as inaccurate and premature.
Seeking to remind voters of Romney's past gaffes, the Obama campaign released a new ad in Virginia, a battleground in the November 6 election, that characterized the Republican challenger as "reckless" and "amateurish" on international affairs.
The 30-second spot features news clips of what the commercial calls Romney's "gaffe-filled" trip to England, Israel and Poland.
"If this is how he handles the world now," the narrator in the new ad says, "just think what Mitt Romney might do as president."
Responding to the ad, a Romney campaign spokeswoman said Obama was the one who had "weakened" the U.S. standing in the world.
On Sunday, Romney foreign policy director Alex Wong told reporters that the candidate's foreign policy seeks the traditional U.S. role in global affairs dating to the end of World War II.
"Mitt Romney's vision is to restore influence and to support our friends and allies to move the Middle East onto a path of greater liberty, greater stability, and greater prosperity," Wong said. "It's a restoration of a strategy that served us well for over 70 years."
Referring to the U.S. perspective after World War II, Wong said that "we saw the need to have a military that no one would challenge." He also cited the need to have strategic allies around the world as part of what he called a full spectrum of power "so we do not have to face again the horrors of war."
Romney and Obama will debate foreign policy on October 22 in Florida following their second debate in New York on October 16. On Thursday, Vice President Joe Biden and Romney's running mate, Rep. Paul Ryan of Wisconsin, will hold their only debate of the campaign.