CAIRO, Egypt -- Two U.S. Senators came to Egypt Tuesday with a message for the country's new military-backed leaders: Release Islamist figures as a gesture to the Muslim Brotherhood or risk making "a huge mistake."

The message from Republican Senators John McCain and Lindsey Graham met with a sharp response, denounced by interim President Adly Mansour in a brief statement as "unacceptable interference in internal politics."

The new leadership, emboldened by mass demonstrations of support, showed no sign of willingness to release Muslim Brotherhood figures whom McCain called "political prisoners" and whom the government plans to prosecute for allegedly inciting violence.

As the senators made their rounds, authorities announced that two Morsi aides would be jailed and face charges of inciting violence in December when Muslim Brotherhood members attacked a sit-in by protesters outside Morsi's office that sparked clashes, killing 10 people.

At stake is stability in the Arab world's most populous country. The new leadership is facing international calls to ease its crackdown on Morsi's group while also dealing with calls by millions of Egyptians to clear Brotherhood-led sit-ins in two major intersections of the capital. Some 250 people have been killed in various clashes since Morsi's ouster.

The Brotherhood is demanding Morsi's reinstatement as Egypt's first freely elected president while the new government vows to push ahead with fresh elections early next year.

The McCain-Graham visit was carried out at U.S. President Barack Obama's request, but their message differed from his. For one thing, they called what happened on July 3 a coup, a word the administration avoided because it would trigger a suspension of the $1.3 billion a year in U.S. military aid to Egypt.

State Department spokeswoman Jen Psaki said "Our position has not changed" regarding the word "coup." "Sen.McCain and Sen. Graham are certainly entitled to their opinions, just as any member of Congress is."

At a news conference in Cairo after meeting government officials, military leaders and members of the Brotherhood's political wing, the senators stressed the need to free prisoners.

"It is impossible to talk with somebody who's in jail. That is not a sustainable model that will allow transition to occur," said Graham.

"The status quo is unacceptable. Something's got to give," he said.

He also said his message to the government is: "If you think you can negotiate with people who are in jail and that's the way you're going to negotiate, you're making a huge mistake."

Echoing that sentiment, McCain said the Brotherhood must be included in Egypt's transition.

"Our purpose is to try to urge our friends toward a process that can avert a very serious situation that can affect not only the Arab world, but also the United States."

Graham suggested that U.S. military aid could be at risk.

"We cannot support Egypt that is not moving toward democracy. Our aid is going to be tied to what's best, from our point of view, for the world, Egypt and the region," he said.

McCain, however, said cutting off aid "would have been the wrong thing to do and the wrong time."

The two Senators also said they made clear that they want the Brotherhood to renounce violence before negotiations start.

McCain and Graham have been preceded by senior officials of the Obama administration, the European Union, oil-rich Arab Gulf states and the African Union, all anxious to stem the crisis.

But Egyptian officials were sounding increasingly annoyed at what they saw as foreign meddling.

Mustafa Hegazy, a political adviser to interim President Mansour, appeared to rebuff the international calls to release detainees, saying those in jail will be dealt with by the law "and not by politics."

"No one can impose their conditions on the future," the state-owned MENA news agency quoted him as saying.

Morsi has been held at a secret location since his ouster. Last week, he was visited by the EU's foreign policy chief Catherine Ashton and a group of African statesmen, but authorities say no more visits will be allowed.

In a sign of domestic pressures on the government to act strongly, Vice-President Mohamed ElBaradei came under heavy criticism for suggesting compromise was needed.

Top officials say reconciliation can only come after the Brotherhood renounces violence. They blame the Brotherhood for sectarian violence in southern Egypt, the torture of anti-Morsi protesters and the blocking of main roads. The government says it has ordered security forces to clear out the pro-Morsi protest camps in Cairo because they pose a "national security threat."

Pro-military writer Gamal Ghitani said the U.S. is seen by many as trying to pressure the government to reverse a decision made by people who rejected the mixing of religion in politics when they took to the streets to demand Morsi's ouster.

While publically demanding Morsi is returned to power, privately many of the pro-Morsi protesters say that the sit-ins are their last bargaining chip to press for the release of detained leaders and for guarantees that they will be included in politics.

Makram Mohammed Ahmed, a political analyst in Egypt, said releasing top Islamist prisoners would mean the collapse of the judicial system because many of those detained are now facing charges of inciting violence against protesters.

"This will not be a state based on laws if these people are released," he said. "The Egyptian people are not happy with the United States or the Obama Administration and do not see fairness in their actions."

Graham said the U.S. has learned from its mistakes when it supported for decades autocratic President Hosni Mubarak, who was deposed in a popular uprising in 2011.

"We are no longer able to side with people who will be just beneficial to us," he said. "The politics of convenience are behind us."