Republicans on Thursday criticized President Obama for not going further to tamp down violence in Egypt, with Sen. Bob Corker (R-Tenn.) saying the administration should be tougher on the Muslim Brotherhood and Sen. Rand Paul (R-Ky.) saying Obama is "skirting" the law and should cease sending foreign aid to the country.

"I appreciated much of what the president had to say, and while it reflected an arms-length disapproval of the military’s actions, I wish he had stressed more clearly the need for the Muslim Brotherhood to also act responsibly," Corker said in a statement.

Paul reiterated his call for cutting off foreign aid to the country. He said that the uprising meets the definition of a coup -- a word that the administration has avoided -- and that status means aid should come to an end.

“The law is very clear when a coup d’état takes place, foreign aid must stop, regardless of the circumstances," Paul said. "With more than 500 dead and thousands more injured this week alone, chaos only continues to grow in Egypt. So, Mr. President, stop skirting the issue, follow the law, and cancel all foreign aid to Egypt.”

At least one Democrat, Rep. Keith Ellison (Minn.), agrees with Paul.

“The Obama administration was right to condemn the crackdown," Ellison said in a statement. "It should also suspend U.S. assistance to Egypt's military until democracy is restored. This would not only make clear that we do not support this type of violent repression, but is also required under U.S. law when a military deposes a democratically elected leader."

A recent Paul-sponsored amendment seeking to cut off Egypt's aid got just 13 votes in the Senate.

Other Democrats praised Obama's remarks.

Sen. Tim Kaine (D-Va.) said Obama hit the right chords during his address, particularly when it comes to stopping joint military exercises with Egypt.

"The president’s announcement that the joint military exercise, Bright Star, would be canceled this year is appropriate as the interim government’s actions run counter to U.S. principles and values," Kaine said.

House Minority Leader Nancy Pelosi (D-Calif.) said: “The President is right to strongly condemn the horrific violence in Egypt and to cancel the joint exercises with the Egyptian military. The continued state of emergency must come to an end."