President Obama hailed Mubarak's decision but also urged that the transition to a new government "must begin now."
"An orderly transition must be meaningful," Obama said in remarks made after Mubarak's speech. "It must be peaceful and it must begin now."
Obama also praised the peaceful demonstrators in Egypt, calling them an "inspiration to people around the world."
"To the people of Egypt, particularly the young people of Egypt, I want to be clear," Obama said. "We hear your voices."
The situation in Egypt is particularly alarming to the United States. Egypt is one of United States' closest allies in the Middle East. It is only one of two Arab countries that recognizes Israel and has helped broker key peace deals. Mubarak's government has also been a close U.S. ally in the fight against terrorism. Egypt is also home to the Suez Canal, and any instability in the region could be gravely dangerous to U.S. interests in the region.
Just hours after Mubarak's speech, Al Jazeera was reporting there were shots fired in Alexandria during violent clashes between pro-Mubarak and anti-government demonstrators.
Yemen's president Ali Abdullah Saleh vowed not to run for re-election in 2013 and also said his son will not seek the presidency. Protests have spurred up in that country in recent weeks, raising concern that the uprising in Egypt and Tunisia could force the government out in Yemen, another U.S. ally.
Jordan's King Abdullah sacked his government Tuesday amid protests that were directed mainly at prime minister Samir Rifai.
After Egypt, Jordan is United States' second biggest ally in the region and only the second Arab country to recognize Israel.
The cabinet of the Palestinian Authority in the West Bank also said it will hold municipal elections "as soon as possible." And in Gaza, which is run by the Islamic group Hamas, demonstrators sympathetic to the Egyptian cause were arrested, according to the Associated Press.
The U.S. government continued to pull its citizens out of Egypt as protests gain momentum. The U.S. Embassy said today it expects to evacuate more than 1,000 Americans over the next two days on special chartered flights. The State Department issued a mandatory evacuation order Tuesday calling for all non-essential U.S. embassy staff to leave.
ABC News' Nasser Atta, Lama Hassan and Alexander Marquardt contributed to this report.