The trip to Cyprus is estimated at about 10 hours, reports CBS News' Kristin Gillespie. Once there, the U.S. citizens will make arrangements to continue on to other destinations, including the United States.
The State Department dropped plans to make the Orient Queen passengers pay for their passage.
Thousands more Americans still want to leave Beirut.
"Today in the port there are six chartered ships that are taking an estimated 30,000 Canadians out of the country, all in one go," reports . "The British and the Europeans are also continuing to evacuate their citizens. They began these efforts last week."
Meanwhile, Israeli troops clashed with Hezbollah guerrillas on the Lebanese side of the border Wednesday, while Israeli bombers flattened 20 buildings and killed at least 19 people, as fighting between the two sides entered its second week.
In other developments:
Americans wiped away tears, hugged relatives and grumbled about evacuation delays Wednesday before boarding the luxury ship that is carrying them from war-torn Lebanon.
A U.S. Marine general coordinating the evacuation from Lebanon estimated Wednesday that more than 6,000 Americans will be taken out of that country by the weekend. Brig. Gen. Carl Jensen also stressed that the U.S. Embassy in Beirut will not close and that America "is not deserting Lebanon."
reports it was a much different scene at Beirut's port Wednesday: "It almost looks like an airport terminal, with a check-in area. There's a huge makeshift tent where people line up. They've got their small, little suitcases with them," Gillespie said.
"In downtown Beirut today, the shops are closed, the streets are relatively empty, and there are hundreds of (Americans) standing around with suitcases," reports Gillespie. "It seems that they're waiting to be picked up, they're waiting to be evacuated."
Many Americans expressed frustration that it had taken the U.S. government so long to get them out of Lebanon.
"I can't believe the Americans," Danni Atiyeh, a 39-year-old civil engineer from Kansas City, Mo., said as he waited with his pregnant wife and sons Ali, 10, and Adrian, 6, for buses that were taking them to the ship. "Everybody else has gone home ... We're still here."
The State Department said it had dropped a plan to make Americans reimburse the government for the trip.
"We want to do everything we can to facilitate the departure of American citizens from Lebanon. Today's step removes one potential worry for our citizens at this difficult time," spokesman Sean McCormack said in a statement.
But Atiyeh said he and others were asked to sign promissory notes to pay for the trip before they could leave.
An estimated 8,000 of the 25,000 Americans in Lebanon want to leave the country, and the Orient Queen only holds 1,000.
In Moshav Avivim, an Israeli town on the border, Israeli soldiers were engaged in a substantial battle with Hezbollah guerrillas, reports
Military officials said Israeli troops crossed the Lebanon border in search of tunnels and weapons. Hezbollah claimed to have "repelled" Israeli forces near the coastal border town of Naqoura. Casualties were reported on both sides.
The Israeli army confirmed there were clashes with Hezbollah in the border area and that some Israelis had suffered casualties. The army would not elaborate. Hezbollah's Al-Manar television channel reported that two Israeli soldiers had been killed and three wounded, but that could not be confirmed.
Israel, which has mainly limited itself to attacks from the air and sea, had been reluctant to send in ground troops because Hezbollah is far more familiar with the terrain and because of memories of Israel's ill-fated 18-year occupation of south Lebanon that ended in 2000.
The fighting dealt a blow to diplomatic efforts to broker a cease-fire and to send a new international force to bolster the 2,000-member U.N. force in south Lebanon appeared stalled.
"The U.N. envoys are expected to return this week and report back on the proposals for a ceasefire and the regional views of a U.N. stabilization force proposed by the Secretary General and Prime Minister Tony Blair," said CBS News foreign affairs analyst Pamela Falk, "a proposal which has already met with some resistance by U.S. Ambassador John Bolton, who said earlier in the week that the mechanisms were already in place under U.N. resolutions to disarm Lebanese militias."
Israel declared Tuesday it was ready to fight Hezbollah guerrillas for several more weeks, raising doubts about international efforts to broker an immediate cease-fire. The fighting has killed nearly 300 people and displaced 500,000.
"It will take us time to destroy what is left," Brig. Gen. Alon Friedman, a senior army commander, told Israeli Army Radio on Wednesday.
Israel stressed it did not plan to target Hezbollah's main sponsors, Iran and Syria, during the current fighting.
"We will leave Iran to the world community, and Syria as well," Vice Premier Shimon Peres told Army Radio. "It's very important to understand that we are not instilling world order."