In an interview with ABC News, Mr Romney described as “inappropriate” a US embassy response to an anti-Islam film which sparked protests.
The Republican candidate added he would like to bring Egypt “closer” to the US.
Polls released a week after the end of the US party conventions show Mr Obama leading nationally and in swing states.
A survey of likely voters shows Mr Obama leading the contest by 3% nationally.
The New York Times/CBS poll also suggested Mr Obama had a strong lead among women, but was less popular with those describing themselves as independents.
A separate poll focussing on swing states seen as crucial to Mr Romney’s election chances suggests Mr Obama is holding slight leads in Florida, Virginia and Ohio.
Foreign policy criticism
Mr Romney has been criticised by pundits and Democrats for attacking the Obama administration before the situation in Egypt and Libya became clear. His actions were also questioned by conservatives and Republicans.
In a statement issued late on Tuesday, he said the administration appeared to “sympathise with those who waged the attacks”.
He was referring to a statement issued by the US embassy in Cairo before protesters there breached the compound – and before it was known Ambassador J Christopher Stevens had been killed in an attack in Libya.
Mr Romney stood by his criticism of the administration as events unfolded on Wednesday, despite a lack of firm support from his Republican party.
In his ABC interview on Friday, Mr Romney said Egypt’s relationship with the US was in flux.
“We recognise that Egypt has gone through a dramatic change in government. And what their status will be going forward in terms of the relationship with our nation is something which I’m sure will be developing over time.
“That being said, I would like to bring Egypt closer to us. I think it’s important for them to understand that it’s an advantage to have a close relationship with the United States, to be an ally of the United States.
Speaking to ABC, Mr Romney said that he was not concerned about the new poll numbers.
“These polls are going to bounce around a lot. I don’t pay a lot of attention day to day to which state’s up and which one’s down,” Mr Romney said.
As the US presidential election is decided by the number and size of the states won by each candidate, analysts are focussing on several key states that could go either way.
Correspondents say that it is very difficult for Mr Romney to become president without winning at least two states among Florida, Ohio and Virginia, while Mr Obama’s has more “paths to victory”.
Friday’s NBC/Wall Street Journal poll suggested Mr Obama was leading Mr Romney in all three states, with a 7% difference between them in Ohio.
The polls emerge as the candidates prepare for the first of three televised presidential debates, to be held on 3 October in Denver, Colorado.
Mr Romney says he is looking forward to chance to debate Mr Obama, but says the president “tends to say thing that are not true”.
“Beating an incumbent is never easy,” he said. “But at the same time, I think people recognize that he has not done the job they expected him to do and that he promised he would do.”
In an interview with CBS News on Wednesday, Mr Obama said that his election opponent had “a tendency to shoot first and aim later”.
“It’s important for you to make sure that the statements that you make are backed up by the facts.”
Mr Romney planned to campaign in New York and Ohio on Friday, shifting back to economic policy.