The 82-year-old president, who has held power for nearly 30 years, said he intends to serve until the next national election this fall.
Mubarak, who fired his Cabinet last weekend, said he would concentrate on social and political reforms, and prepare for the transfer of power to the next government, The Washington Post reported.
He said while people have the right to demonstrate peacefully, the protesters have been "exploited by those who wanted to create chaos and destroy the constitution." Egyptians, he said, must choose "between chaos and stability."
The president, who has a military background, told the nation he has fought for Egypt "and I will die on its land."
He also said it was "not in my nature to give up responsibility."
"I never wanted power or prestige," Mubarak said. "My first responsibility now is to restore the security and stability of the homeland to achieve a peaceful transition of power in an environment that will protect Egypt and the Egyptians, and which will allow for responsibility to be given to whoever the people elect in the forthcoming elections.
"I want to say in clear terms that in the next few months remaining in my current term, I will work very hard to carry out all necessary measures to transfer power ... ."
The Los Angeles Times reported its sources said Mubarak rejected a message delivered by special U.S. envoy Frank G. Wisner urging him to stand down.
Whether Mubarak's announcement would satisfy the protesters who have taken to the streets of Egypt's major cities in extraordinary numbers for the past week and the rest of Egypt's 80 million people remains unclear, the Post reported. The protesters cheered and wave flags upon hearing Mubarak's speech but the Post said initial reports were that many still want him to step down now.
USA Today reported that at dusk the protesters began singing Egypt's national anthem.
It's what comes after Mubarak's departure that concerns many Egyptians, the newspaper said.
"If he leaves power, this country will be lost," Sayed Naguib, 34, a filmmaker, said. "We've been living for 30 years in peace, without war."
U.S. State Department spokesman Philip J. Crowley said all non-emergency U.S. government personnel and their families have been ordered to leave Egypt.
He said the department will facilitate the evacuation of U.S. citizens who require assistance.
The demonstrators appeared to cut across lines of age, education, religion and station in life, the Times reported.
"Leave Mubarak," they chanted. "We don't want you."
Businessman Ahmed Ali said he was inspired to join the protests because he was tired of paying government kickbacks. A 22-year-old tennis coach identified only as Mohammed said he was demonstrating over the lack of jobs.
"We can't find work. We have problems with bread, problems with electricity," he said. "Our biggest problem is to get Mubarak to go away."
The international pressure on Mubarak to resign included Turkish Prime Minister Recep Erdogan, who offered this assessment: "No government can survive against the will of its people. The era of governments persisting on pressure and repression is over. … We are all passing and will be judged on what we leave behind."
The Post said the atmosphere among the protesters in Cairo was festive, with people waving flags, signs and banners, including one that simply said "Get Out." Several demonstrators carried a fake coffin with the words "Hosni Mubarak" written on it, the Post said.
"Washington has been very anxious about what's happening here. But it shouldn't be anxious. It should be happy," Mohammed Fouad, a 29-year-old software engineer, told the Post. "This will reduce terrorism. When people have their voice, they don't need to explode themselves."
Banks, the stock market and schools were closed, and the government-imposed overnight curfew has been routinely ignored. The country's airspace was closed and nationwide train service was suspended during curfew hours.
Some activists communicated through old dial-up Internet services reached through international phone numbers, the Times said. Others posted Twitter messages by calling an international number and leaving a voice mail message that was then posted on Twitter through a new "speak-to-tweet" service developed with Google.
The military said Monday it would not open fire on peaceful protesters, various media reported.
Human Rights Watch staff said the organization confirmed 80 deaths from two hospitals in Cairo, 36 deaths in Alexandria and 13 fatalities in Suez.
The White House wants Mubarak's departure "sooner rather than later," the Post reported. The European Union also called for "free and fair elections" in Egypt.