Secular and liberal factions in Egypt’s new leadership worked Sunday to reach a compromise with ultraconservative Islamists on a new prime minister, with a liberal economist emerging as a leading candidate for the post to run the country after the military’s ouster of President Mohammed Morsi.

As the negotiations continued over the post, the shows of strength over the removal of Egypt’s first freely elected president were far from ending, with hundreds of thousands in the streets Sunday from each side. The military deployed troops at key locations in Cairo and other cities amid fears of renewed violence.

The Muslim Brotherhood pushed ahead with its campaign of protests aimed at forcing Morsi’s reinstatement, bringing out large crowds in new rallies. Its officials vowed the group would not be “terrorized” by arrests of their leaders and the shutdown of their media outlets.

The Brotherhood’s opponents, in turn, called out large rallies in Tahrir Square and other squares in Cairo and several cities to defend against an Islamist counter-push. The rallies took on a sharply nationalist tone — with effusive praise of the military and strong anti-American sentiment over perceived U.S. support for Morsi and his Brotherhood.

Military warplanes swooped over the crowd filling Tahrir, drawing a heart shape and an Egyptian flag in the sky with colored smoke. In the square, large banners read “Obama, hands off, a message to the USA. Obama supports the terrorists of 911” with a picture of Obama with an Islamists’ beard.

The tone appeared aimed at drowning out cries from the Brotherhood and its Islamist allies that the army’s toppling of Morsi was a coup against democracy. The anti-American slogans had a double-edged message: painting the Brotherhood as a tool of Washington and pushing back against U.S. concerns over the military’s moves here.

Throughout Morsi’s year in office, many of his opponents accused the United States of backing his administration. Washington often underlined that it was dealing with Morsi as the country’s elected leader. Before the wave of anti-Morsi protests began on June 30, U.S. Ambassador to Egypt Anne Patterson said in a speech that she was “deeply skeptical” protests would be fruitful and defended U.S. relations with Morsi’s Muslim Brotherhood as necessary because the group is part of the democratically elected Egyptian government.

Since Morsi’s removal Wednesday, the U.S. has tread carefully, expressing concern without outright calling the army’s move a coup or denouncing Morsi’s ouster. On Saturday, the White House said in a statement that it rejects “false claims propagated by some in Egypt that we are working with specific political parties or movements to dictate how Egypt’s transition should proceed,” saying it is committed to Egyptians’ aspirations for democracy.

The Islamists have denounced the removal of Morsi as an army coup against democracy. Their opponents have argued the president had squandered his electoral mandate and that the Brotherhood was putting Egypt on an undemocratic path.

Pro-Morsi rallies turned out in several places around the city Sunday, centered outside the Rabaah al-Adawiya Mosque where they have been holding a sit-in for more than a week.

In a Facebook posting Sunday, the Brotherhood’s supreme leader Mohammed Badie said the “leaders of the unconstitutional coup continue flagrant violations against the Egyptian people.”

Senior Brotherhood member Saad Emara said there was no possibility for any negotiations with the new leadership after “all betrayed us,” and following the military’s clampdown on the group.

“We are not regressing to a Mubarak era but to … a totalitarian regime,” he said. “Anything other than protest is suicide.”

Morsi and five top Brotherhood figures are currently in detention, and around 200 others have arrest warrants out against them. The group’s TV station and three other pro-Morsi Islamist stations were put off the air. Among those detained is Badie’s deputy Khairat el-Shater, seen as the most powerful figure in the group and its main decision-maker.

A Brotherhood spokesman, Gehad el-Haddad, said the military is not giving any positive signals for the group to be willing to talk, pointing to the arrests of the leadership figures and shutdowns of media.

“They are trying to terrorize us,” he said.