Two US senators urged Egypt's military-backed government to release detained members of the Muslim Brotherhood before starting negotiations with the group, warning of worsening relations "if Egypt is not moving to democracy."
But Egypt's interim presidency denounced "foreign pressure" in a sign of its growing impatience with international mediations.
Sens. John McCain and Lindsey Graham spoke after meeting with top military and civilian leaders in Cairo as part of a flurry of international efforts to resolve a standoff between the government and supporters of the ousted president, Mohamed Morsi.
McCain said "we urge the release of political prisoners," referring to Brotherhood members who were detained after the military ousted Morsi, an Islamist, a month ago.
"In democracy, you sit down and talk to each other," Graham said, adding, "it is impossible to talk to somebody who is in jail."
Graham warned that US-Egyptian relations might otherwise be harmed.
"Some in Congress want to sever the relationship. Some want to suspend the aid," he said. "We have to be honest to where the relationship stands. ... We can't support Egypt that is not moving to democracy."
McCain and Lindsey Graham have also described the army's removal of Morsi as a coup.
Egypt's new government has held firm to a political road map announced July 3, when the military ousted Morsi following mass protests calling on him to step down.
US and other international officials have urged the inclusion of Morsi's Muslim Brotherhood in the political process going forward.
Top Egyptian officials said reconciliation is a priority but only after the Brotherhood renounces violence. They cite sectarian violence in southern Egypt, cases of torture of anti-Morsi protesters and the blocking of main roads.
Ahmed El-Muslimani, a spokesman for interim president Adly Mansour, told reporters that "foreign pressure has exceeded international standards." He said Egypt will protect "the revolution" — referring to June 30, the day hundreds of thousands of Egyptians revolted against Morsi's rule.
El-Musalamani didn't elaborate. However, his comments came as the country's powerful military chief Gen. Abdel Fattah El-Sissi and Vice President Mohamed ElBaradei held separate meetings with Graham and McCain, who arrived in Cairo on Monday at President Barack Obama's request to press senior Egyptians for a quick return to civilian rule.
Egypt's official news agency MENA reported that the two Republican senators and El-Sissi discussed efforts to end "the state of political polarization and stop the violence" while moving forward with Egypt's fast-track road map. The plans calls for amending the constitution and holding new elections by early next year "without discrimination or isolation."
US Deputy Secretary of State William Burns, who arrived Friday, also was meeting with Mansour and ElBaradei.
Early Monday, Burns visited Khairat El-Shater, a top Muslim Brotherhood leader who is held in a Cairo prison. He was accompanied by a European Union envoy and Gulf foreign ministers.
Morsi, Egypt's first freely elected president who came to power nearly a year and a half after the ouster of his predecessor Hosni Mubarak in a 2011 uprising, 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 the administration has said it will not allow any more envoys to visit him.
All talks are centered around averting collision between the military-backed government and Muslim Brotherhood supporters. They have been camping out in Cairo and its sister city of Giza for more than a month demanding Morsi's reinstatement as well as the return of the constitution and the parliament.
The protest camps have been used as a hotbed for street marches that blocked traffic and sometimes sparked street violence either with security forces, or Morsi's opponents.
In two incidents this month, more than 130 people, mostly Morsi supporters, were killed in clashes near their main sit-in in eastern Cairo.
The government said that it has ordered the security forces to clear out the protest camps because they pose "national security threat."
The Muslim Brotherhood publicly says it rejects any concessions and that its starting point would be Morsi's return to power. Privately, though, protesters say that the camp is their last bargaining
chip to press for the release of detained leaders and for guarantees that they will be included in politics.
A European Union official in Brussels has said diplomats were working on confidence-building measures such as releasing detained Brotherhood officials, dropping charges against other group members and dispersing the pro-Morsi sit-ins held at two squares on opposite ends of the Egyptian capital.
The official spoke on condition of anonymity to brief reporters on the confidential discussions.
In an official statement after meeting with Burns on Tuesday, ElBaradei stressed that Egypt's "priorities are to secure citizens and protect their lives, their possessions and to preserve security and law ... while moving forward to achieve comprehensive political reconciliation."