The politicians who attended the discussions in Cairo also said that a parliamentary election, scheduled to start on Nov. 28, would go ahead as scheduled after violence during protests against the ruling military council cast doubt on its timing.
"Presidential elections to be held by the end of June and the final preparations for handing over power by July 1," Emad Abdel Ghafour, head of ultra-conservative Nour (Light) party, told Reuters, adding that he expected the vote on June 20.
Other politicians also said the election would be held by July 1, but did not give a date for the voting.
Aboul-Ela Madi and Mohammed Selim el-Awa, two politicians who attended a five-hour crisis meeting with the military rulers, said the generals accepted the resignation of Prime Minister Essam Sharaf's government and will form a "national salvation" Cabinet to replace it.
Prime Minister Sharaf offered his government's resignation on Monday. There has been no official announcement, however, about whether it had been accepted.
Abdel Ghafour also said controversial proposals put forward by the outgoing army-backed Cabinet that would have would have permanently shielded the military from civilian oversight under a new constitution had been dropped.
Egypt's military head of state, Field Marshal Hussein Tantawi, was expected to address the nation as protests in Cairo and other major cities carried on for a fourth day.
American students arrested
Egyptians were converging on Cairo's central Tahrir Square in response to a call for a so-called "million-man march."
Security forces stayed out of Tahrir Square itself to lower the temperature. But there were clashes on side streets leading to the square - the epicenter of the uprising that ousted longtime authoritarian leader Hosni Mubarak in February.
Three American students at the American University of Cairo, which sits on Tahrir Square, were arrested outside the university's campus Monday night, Morgan Roth, a spokeswoman for the university, told NBC News.
She did not specify whether any charges had been filed or what any charges may be, but she named the three students as Luke Gates, an Indiana University student from Bloomington, Indiana; Gregory Porter, a Drexel University student from Glenside, Pennsylvania; and Derrik Sweeney, a Georgetown University student from Jefferson City, Missouri.
The three were on a study abroad program with the American University of Cairo.
They were being held at the Abdeen police station in Cairo, NBC reported.
© Khalil Hamra/APA riot police officer fires tear gas during clashes with protesters near Tahrir Square in Cairo on Tuesday.
George Gates, the father of a 21-year-old Luke Gates, also confirmed to NBC that his son had been arrested "sometime late last night," and said the family was in contact with the Department of State.
On what appears to be Luke Gates' Twitter feed, Gates lists his location as Cairo, Egypt and makes references to being in Tahrir Square.
His last post, dated Monday, November 21, read, "reports of tear gas being fired from AUC campus on Tahrir, university officials have started investigating."
An airport official also said a U.S. citizen who had been arrested while allegedly filming security forces at Tahrir Square was deported Tuesday to the United Arab Emirates from which he had arrived.
State television showed brief footage of the three students, males who appeared to be in their early 20s.
Elections coming
The new wave of protests and violence around the country that began on Saturday has left 29 dead and has thrown Egypt's politics into chaos less than a week before landmark parliamentary elections were to begin.
"The army is making the same mistake as Mubarak. They hear the demands but respond when it's too late," said protester Mustafa Abdel-Hamid, a supporter of the Muslim Brotherhood who came to Tahrir even though his movement has not endorsed the protests over the past four days.
© Microsoft/NavteqProtest Centers in Egypt.
The crowds carried an open wooden coffin with a body of a slain protester wrapped in white and held a funeral in the middle of the square.
A stuffed military uniform was hung from a central light pole with a cardboard sign on its neck saying "Execute the field marshal," a reference to Tantawi, Mubarak's defense minister of 20 years. People cheered when the effigy was hung and state television showed some hitting it with sticks.
Men in the square opened a corridor in the middle of the crowds and formed a human chain to keep it open, giving easy access to motorcycles and ambulances ferrying the wounded to several field hospitals in the square.
Battered economy
Egypt's military has been backed into a difficult corner. Protesters are demanding it surrender the reins of power - or at least set a firm date in the very near future for doing so soon. Without that, few civilian political leaders are likely to join a new government for fear of being tainted as facades for the generals, as many consider the current Cabinet.
The office of leading pro-reform activist Mohamad ElBaradei said the Nobel Peace Laureate did not attend the crisis meeting but was in touch with the military. ElBaradei prefers to continue to act as the link between the military council and the protesters until the crisis is resolved, his office said.
ElBaradei's name has been mentioned by protesters as a suitable replacement for Prime Minister Essam Sharaf, who was under intense criticism for the perceived inefficiency of his civilian government and for being beholden to the ruling generals.
© Microsoft/Navteq/GeoeyeTahrir Square from above.
Egypt's benchmark index plunged more than 5 percent, the third straight day of declines. Banks closed early and many workplaces sent employees home ahead of schedule for fear of a deterioration in security.
Several main roads were closed to traffic, adding to Cairo's already congested streets.
'Deplorable' violence
The United States, which gives Egypt's military $1.3 billion a year in aid, has called for restraint on all sides and urged Egypt to proceed with elections.
"We are deeply concerned about the violence. The violence is deplorable. We call on all sides to exercise restraint," White House spokesman Jay Carney told reporters Tuesday.
Political uncertainty has gripped Egypt since Mubarak's fall, while sectarian clashes, labor unrest, gas pipeline sabotage and a gaping absence of tourists have paralyzed the economy and prompted a widespread yearning for stability.
Meanwhile, rights group Amnesty International accused Egypt's rulers on Tuesday of brutality sometimes exceeding that of Mubarak, saying the hopes of protesters had been "crushed."
The group said Egypt's Supreme Council of Armed Forces (SCAF) - which assumed control after an 18-day uprising toppled Mubarak in February - had made only empty promises to improve human rights.
In a report, Amnesty said military courts had tried thousands of civilians and emergency law had been extended. Torture had continued in army custody, and there were consistent reports of security forces employing armed "thugs" to attack protesters, it added.
"The SCAF has continued the tradition of repressive rule which the January 25 demonstrators fought so hard to get rid of," said Philip Luther, Amnesty's Middle East and North Africa acting director.
"Those who have challenged or criticize the military council - like demonstrators, journalists, bloggers, striking workers - have been ruthlessly suppressed in an attempt at silencing their voices ... The brutal and heavy-handed response to protests in the last few days bears all the hallmarks of the Mubarak era."
By August, Amnesty said the military council admitted about 12,000 civilians had been tried by military courts and at least 13 sentenced to death. The trials were "grossly unfair", said the rights group.
The Associated Press and Reuters contributed to this report.
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