By Steve Holland

NEW YORK, Sept 14 (Reuters) - Egypt needs to ensure the security of foreign diplomats or risk losing the $1.3 billion in aid it receives each year from the United States, Republican presidential candidate Mitt Romney said on Friday.

After Islamist protesters breached the U.S. Embassy in Cairo this week, Romney told a fundraising breakfast in New York the United States should take a tougher line with Egypt.

"I think for instance in Egypt we should make it very clear to maintain a relationship, a friendship, an alliance and financial support with the United States, Egypt needs to understand it must honor its peace treaty with Israel, he said.

"It must also protect the rights of the minorities in their nation. And finally among other things it must also protect the embassies of our nation and other nations," he said.

Egyptians angry at a film they said was blasphemous to Islam clashed on Friday in Cairo for a third day with police who blocked the way to the U.S. Embassy, where demonstrators climbed the walls and tore down the American flag earlier this week.

Four Americans, including the U.S. ambassador, were killed in Libya in related violence.

The United States gives $1.3 billion in military aid a year to Egypt, plus other assistance.

"The American people are disturbed and reeling with the news around the world," Romney told the fundraising event, which brought in $4 million for his campaign, for a two-day regional haul of $7.5 million.

A number of polls this week showed Obama building a lead over Romney after the Democratic National Convention last week but the Republicans' advisers insist the race is close and the former Massachusetts governor remains in solid shape with less than two months to go until the Nov. 6 election.

Romney, an advocate for a strong relationship with Israel, criticized Obama for deciding not to meet with Israeli Prime Minister Benjamin Netanyahu when the two leaders are in New York this month for the annual U.N. General Assembly.

The presidential race thus far has been dominated by questions over how to rekindle strong growth in the U.S. economy, a challenge that plays to Romney's strengths as a former business executive.

Romney's vice presidential running mate, Paul Ryan, a budget expert who lacks foreign policy experience, also jumped into the Mideast debate.

"We have all seen images of our flag being burned and our embassies under attack by vicious mobs," he told a conservative group in Washington on Friday.

"Amid all these threats and dangers, what we do not see is steady, consistent American leadership," he told the Values Voter Summit meeting. "In the days ahead, and in the years ahead, American foreign policy needs moral clarity and firmness of purpose," he said.