His warning came as the United States toughened its line on Mubarak's government, a key Middle Eastern ally, warning it would review billions of dollars in aid to Egypt based on the behavior of the security forces.
Obama urged Mubarak to take "concrete" steps towards political reforms, saying he must turn "a moment of volatility" into "a moment of promise" after a day of rage in Egyptian cities on which the death toll from protests hit 27.
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"I want to be very clear in calling upon the Egyptian authorities to refrain from any violence against peaceful protesters," Obama said, after aides said the White House was readying for any possible political scenarios in Egypt.
"The people of Egypt have rights that are universal. That includes the right to peaceful assembly and association. The right to free speech and the ability to determine their own destiny."
Obama said he talked to Mubarak after he made a broadcast to the Egyptian people, in which he gave no sign of standing down, but promised to move towards democracy and more economic opportunity for his people.
"I told him he has a responsibility to give meaning to those words," Obama said, in a statement in the State Dining Room of the White House.
"Violence will not address the grievances of the Egyptian people. And suppressing ideas never succeeds in making them go away."
Deploying American leverage
Egypt is the second highest beneficiary of US foreign aid, so the US warning that an average of $2 billion in annual assistance could be in play appeared to be a significant attempt to deploy American leverage.
"We will be reviewing our assistance posture based on events that take place in the coming days," White House spokesman Robert Gibbs said.
"We are watching very closely the actions of the government, the police, the security forces and all those in the military," Gibbs said.
Mubarak has been a fulcrum of US Middle East policy for decades, and is a key player in regional peace efforts and a partner for Washington in its global anti-terror campaign.
US military aid to Egypt amounts to some $1.3 billion annually, most of which is spent on modernizing weapons systems, according to a Congressional Research Service report.
Critics of the US administration had complained in recent days that its response to rising unrest was too tepid, motivated more by a desire to retain a key regional security ally than its call for "universal" human rights.
But Gibbs denied the Obama administration's response to the crisis so far had been equivocal and too restrained.
Unprecedented shutdown of Internet
The Egyptian government's unprecedented shutdown of Internet access also came under fire in Washington and from social networking giants and digital rights groups.
Obama and Secretary of State Hillary Clinton called on the Cairo government to restore the Internet and social networking sites while Gibbs took to Twitter with a similar message.
Facebook, the world's largest social network with nearly 600 million members, and Twitter also weighed in on the digital crackdown.
"The Internet provides people around the world with the power to connect, to learn, and to share," Andrew Noyes, a Facebook spokesman, said in a statement.
"A world without the Internet is unimaginable," Noyes said.
Twitter, which has more than 175 million registered users, said of efforts to block the service in Egypt: "We believe that the open exchange of info & views benefits societies & helps govts better connect w/ their people."
In an accident of timing, the Egyptian army's chief of staff Lieutenant General Sami Enan, was in Washington as the turmoil unfolded, and hurriedly cut short his visit.
Earlier, Obama's daily national security briefing turned into a 40 minute rundown of the situation in Egypt, after he received an in-depth memo on fast-fast moving crisis overnight.
Top officials including National Security Advisor Tom Donilon, top counter-terrorism advisor John Brennan and Robert Cardillo, deputy director of National Intelligence for Intelligence Integration joined the meeting.
In another sign of the worsening situation, the State Department warned Americans against "non-essential travel" to Egypt, the Arab world's most populous country.
