More than 1,200 have already left the country on nine flights headed for Larnaca in Cyprus, Istanbul and Athens, spokesman Philip Crowley said.
Cypriot officials said the first US evacuees had arrived in Cyprus -- 42 US embassy staff and their dependents aboard a military aircraft. A charter flight carrying 180 passengers, most of them Americans, was due later in the day.
At least six more flights were planned on Tuesday, and about 40 extra consular staff had been deployed to Cairo and the three arrival points in a bid to speed up the evacuations, he added.
"Roughly 2,600 people have contacted by a variety of means and registered with us that they wish to leave the country," Crowley said.
"Obviously, today we`ve, kind of, put a pretty good dent in that number, but, obviously, that will... fluctuate day to day, as American citizens make their own decisions about whether to stay in Egypt or to leave."
The United States and several other countries have asked the Mediterranean island of Cyprus to serve as an evacuation hub.
Cyprus expects around 700 foreign nationals to arrive from Egypt on eight flights over the next day or so amid growing unrest in the biggest Arab nation, public radio said. Larnaca is just under 90 minutes` flying time from Cairo.
The island nation became a safe haven for thousands of foreigners when the Israeli bombing of Lebanon in the 2006 war against Hezbollah prompted the biggest maritime evacuation since World War II.
"We are making a huge effort to line up charter flights to take out American citizens who don`t have other means for leaving the country," Assistant Secretary of State Janice Jacobs told CNN earlier.
But she stressed the process -- restricted to non-curfew hours -- could take several days.
"We want to make sure that anyone who needs our help is getting that, and so, yes, I do expect those numbers to go up over the next few days," she added.
The measures came after a seventh straight day of nationwide protest against President Hosni Mubarak`s three-decade rule that have shaken Egypt, and left at least 125 people dead as the veteran leader clings to power.
The angry protests have rocked Cairo by day, while tensions soar at night as neighborhoods try to guard against looters.
About 52,000 Americans are registered with the US embassy in Cairo, but Jacobs said she did not foresee all them wanting to leave.
Among those requesting evacuation assistance, "priority will be given to persons with medical emergencies or severe medical conditions," the US embassy in Cairo said in a statement.
All those traveling aboard the US-arranged flights are expected to pay the equivalent of a commercial fare and would need to make their own arrangements for traveling on from the European destinations.
The State Department was employing "every communications medium -- websites, email, call centers, radio and TV to get information out to US citizens on the ground in Egypt who are understandably worried," Jacobs said.
She noted that the Egyptian government`s Internet shutdown "makes our job more difficult."(*)
Editor: Aditia Maruli Radja
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