Earlier in the day, Suharto, a 76-year-old former army general, was stripped of the support of his most senior political allies in Parliament.
But Indonesia's military chief indicated that Suharto should stay in power for now and carry out a planned Cabinet shuffle while implementing political reforms.
Military chief Gen. Wiranto is the commander of a 400,000-member army which plays a pivotal role in Indonesian politics. On Monday, he warned that plans for big anti-government demonstrations would lead to chaos, and he said the military would deal harshly with rioters.
With government unity unraveling, Suharto held urgent talks with his vice president and key Cabinet ministers, while an aide said he would respond to the parliamentary challenge on Tuesday.
At a summit in London, President Clinton said Monday that Indonesians should decide who leads the country. Though he did not directly call for the president's ouster, Mr. Clinton laid blame at Suharto's feet.
"The absence of a sense of political dialogue and ownership and involvement obviously has contributed to the difficulties there," Mr. Clinton said.
Meanwhile, Parliament speaker Harmoko said the five factions in Parliament would meet Tuesday to ask Suharto, who has led Indonesia for 32 years and is Asia's longest-serving leader, to resign.
CBS News Correspondent Barry Petersen reports that Monday was a day when students kept the pressure on, gathering at campuses around Jakarta, and then as they promised to do, making their way to the Parliament Building. There, they were met by police and the army. But, in the end, the army gave way, peacefully, allowing the students by the hundreds to pour into the Parliament Square and shout for government reform - and the ouster of Suharto.
Rais said he plans to summon 1 million people into the streets of the capital for demonstrations on Wednesday, the 90th anniversary of the nationalist movement against Dutch rule. (Rais heads Muhammadiyah, a Muslim group with 28 million members.)
There was sadness as well on Monday, reports Petersen. The unidentified bodies of those who were killed in the looting or burned alive in the fires were buried Monday.
The caskets were loaded into ambulances and taken to a cemetery outside Jakarta where they were buried, the price of Indonesia's turmoil.
The violence of the past week was triggered by an economic crisithat has pushed up food and fuel prices. At least 500 people are dead, and Indonesian officials say the riots caused at least $250 million in damage. The crisis has loosened Suharto's hold on Indonesia, the fourth most-populous nation on Earth.
The Jakarta stock exchange was open Monday, but trading was light as nervous investors stayed out of the market. Key Asian markets slid in early trading because of fears of continuing turmoil in Indonesia.
Suharto has said he will reshuffle his Cabinet, which critics say is a symbol of nepotism and corruption. It includes his eldest daughter, Siti Hardiyanti Rukmana, who is social affairs minister.
Abdul Latief, the tourism, arts and culture minister, submitted his resignation Monday, apparently the first Cabinet casualty.