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Lawmakers and other officials stepped up calls Thursday for the United States to put heavy pressure on the governments whose people are storming U.S. diplomatic posts across the Middle East and North Africa -- even if it means freezing aid and expelling diplomats from Washington.

The calls increased as anti-American demonstrations and attacks spread to Yemen, and as protests entered their third day near the U.S. Embassy in Cairo, Egypt. The clashes continued, after four Americans including the U.S. ambassador were killed Tuesday night during attacks on the U.S. Consulate in Benghazi, Libya. The attack came roughly a year after the U.S. and its allies helped Libyans overthrow dictator Muammar Qaddafi.

Rep. Peter King, chairman of the House Homeland Security Committee, told Fox News that President Obama should be putting particular pressure on Egypt and its president, Mohammed Morsi, over the sustained demonstrations there. King said the U.S. should suspend aid to Egypt until Morsi makes "absolutely clear" he is condemning the demonstrations and taking "forceful action" to protect the U.S. Embassy.

Obama, in an interview with Spanish-language network Telemundo, pushed back on the idea of suspending aid, saying the U.S. "doesn't have an option of withdrawing from the world."

On Egypt, he said pointedly: "I don't think that we would consider them an ally, but we do not consider them an enemy."

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King countered: "If he's not an ally, why do we continue to give him billions of dollars in aid?"

Egypt was slated to receive $1.6 billion this year in U.S. aid. Protesters earlier in the week stormed the U.S. Embassy in Cairo and tore down the U.S. flag.

Other officials said the U.S. needs to make clear to these countries that they are accountable for what happens at the U.S. embassies.

"When you attack an embassy, you're attacking America," Sen. James Inhofe, R-Okla., told Fox News.

John Bolton, former U.S. ambassador to the United Nations under the George W. Bush administration, said Obama should communicate privately to Egypt and Libya that if this happens again, "we're cutting off all assistance."

"That message has to go all across the Middle East," he said.

Some lawmakers were trying to carve out U.S. aid to Libya in the stopgap funding bill hitting Capitol Hill this week.

The House approved the $1.047 trillion bill in a 329-91 vote.

Rep. Michael McCaul, R-Texas, went further, saying Wednesday that the U.S. should send a signal that "this barbaric behavior will not be tolerated" by suspending aid, closing U.S. embassies in Egypt and Libya and expelling their diplomats from the U.S.

King, though, said the fledgling government in Libya should be treated a little differently.

He said the U.S. might "reconsider" aid, but stressed that the government is fragile there -- and still forming after the downfall of Qaddafi -- and that Libyan security personnel did try to protect Americans during the Benghazi attack Tuesday night.

Secretary of State Hillary Clinton said Wednesday that the U.S. should distinguish the government and people of Libya from the "small and savage" group that launched the attack on the consulate. A number of officials stressed that the relationship with a new Libya must endure despite the attack.

Obama called the presidents of both Libya and Egypt on Wednesday about the demonstrations and attacks.

According to the White House, Morsi "expressed his condolences for the tragic loss of American life in Libya and emphasized that Egypt would honor its obligation to ensure the safety of American personnel."