Egypt's military rulers have now agreed to form a new government and promise to transfer power to a civilian body by July. But tens of thousands of protesters want an immediate end to military rule.

Large crowds of protestors in Tahrir Square in Cairo are demanding the nation's military rulers step down.

And the violence that has accompanied the protests worries U.S. officials.

White House spokesman Jay Carney said, "The United States continues to believe that the tragic events, that these tragic events, rather, should not stand in the way of elections and a continued transition to democracy."

Egypt is the anchor of American foreign policy in the Middle East and its strategic importance is huge, says University of Maryland professor Shibley Telhami. "Egypt is the most populous and influential Arab state. What happens there will be consequential for other American interests, including in the Gulf, how the Gulf States will behave or how they will interpret it. So for all these reasons there is much at stake for the U.S," he said.

Telhami says the continuing clashes between demonstrators and security forces could impact public opinion in the U.S. "If the relationship is stressed and there is a real confrontation between the military and the public you are going to have a changed political environment here both in Congress and in our public opinion," he said.

President Barack Obama has urged Egypt's military council to end emergency rule and halt military trials of civilians.

The violence jeopardizes billions of dollars in U.S. aid to Egypt, says Steven Heydemann of the U.S. Institute of Peace. "We need to be reminding the Supreme Council constantly that they are in a transitional role, that they are in caretaker role and that they should do nothing that would jeopardize the consolidation of an inclusive, tolerant, democratic political system in Egypt," he said.

But too much pressure on the military council could lead to unintended consequences and undermine Egypt's relations with Israel, says Tawfik Hamid, a senior fellow at the Potomac Institute. "Pressuring the military now too much can really, at the end, [result in that] they may face the Islamists controlling Egypt," he said.

The latest demonstrations are the largest to take place since protests forced former President Hosni Mubarak to resign earlier this year.