An eight-deck cruise liner carrying more than 1,000 Americans sailed out of Beirut's port Wednesday, the first mass U.S. evacuation from Lebanon since Israeli airstrikes started more than a week ago.

Dozens of Americans waved from the top decks of the Orient Queen as the luxury ship blew its horn. U.S. Ambassador Jeffrey Feltman waved back from the dock below.

"We expect this to go on for the next week until every American who has asked us for help to leave, gets to leave," Feltman said.

Many of those aboard were relieved to depart, after complaints of slow action by the United States compared to European countries that sent cruise ships, ferries and warships over the past three days to move out thousands.

Just moments before the Orient Queen, a Greek vessel left Beirut carrying as many as 500 Europeans, ship owner ANEK Lines said. Denmark evacuated more than 4,000 of its citizens Wednesday; Australia, Belgium, Britain, Canada, Germany and India were among nations either evacuating citizens or preparing to.

The Americans also stepped up evacuations Wednesday by military aircraft from their hilltop embassy. Chinook transport helicopters ferried 200 Americans from Beirut to nearby Larnaca airport in Cyprus. The Chinooks can carry twice as many people as the Sea Stallion choppers used earlier in the week.

U.S. Brig. Gen. Carl Jensen, who is coordinating the evacuation, estimated that more than 6,000 Americans will have been evacuated by the weekend, most of them on ferries and Navy ships.

Despite the increased efforts, some expressed frustration.

"I can't believe the Americans," said Danni Atiyeh, a civil engineer from Kansas City, Mo., waiting earlier Wednesday with his pregnant wife and sons, ages 6 and 10, for a bus to take them to the cruise ship. "Everybody else has gone home ... We're still here."

The U.S. State Department said Tuesday it had dropped a plan to make Americans reimburse the government for the transport, 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 U.S. citizens in Lebanon want to be evacuated, but Jensen emphasized that the U.S. Embassy in Beirut will not close and that America "is not deserting Lebanon."

"We are assisting those Americans who choose to leave. Many, many are choosing to stay," the general said at the airport in Larnaca.

Phone calls went out to those chosen to leave on the Orient Queen early Wednesday, telling them to gather in northern Beirut to board buses. By 7 a.m., about 400 people were at the meeting place; some families went even earlier right to the port, confused on where to go.

There were tears as relatives dropped off departing Americans, many of Lebanese descent, as well as nervous moments. A woman waiting to have her passport checked burst into tears when a loud explosion from an Israeli airstrike shook Beirut.

"I'm so relieved, there are no words to explain. I'm very thankful," said Elizabeth Kassab, 45, sitting on the deck of the Queen Orient, smoking a cigarette. "But I'm still nervous, and I won't relax until we get out of here."

On Tuesday, the U.S. ambassador pledged that by the end of the week the evacuation would be ramped up to 1,000 Americans a day. He said the evacuation's slow start was intended to safeguard Americans.

"We at the embassy don't have the experience to move a lot of people. Luckily, the U.S. government does," Feltman said. "Security and safe travel were what's on our minds."

Also delaying the Orient Queen was Israel's blockade of Lebanon's ports, part of its campaign of retribution after Hezbollah captured two Israeli soldiers on July 12 in a cross-border raid. Lebanon's only international airport has been shut since Thursday when Israeli jets bombed all three runways.

The Orient Queen had been on a cruise of the eastern Mediterranean when Israel's military campaign began, and Israeli ships detained it Tuesday from sailing in from Cyprus because of Lebanese on board.

Ron Gidor, spokesman for the Israeli Foreign Ministry, said it took a "stupendous amount of coordination" to arrange for ships to evacuate foreigners. Speaking to the British Broadcasting Corp., he said Israel had been in contact with 20 countries.