Pittsburgh, Pennsylvania (CNN) -- More than 50 Haitian children -- rescued from an orphanage damaged by last week's earthquake --arrived Tuesday in Pennsylvania, most of them headed eventually to adoptive homes.
Gov. Edward Rendell, who traveled to Haiti to accompany the orphans back to his state, said the 53 children from the Bresma Orphanage in the Haitian capital of Port-au-Prince were flown to Florida on an Air Force C-17 transport plane. The group was then transferred to another plane to fly to Pittsburgh International Airport, he said at a news conference at the airport.
Another child is to arrive in Pittsburgh late Tuesday or Wednesday, Rendell said. Ali McMutrie, a Pittsburgh-area woman who ran the orphanage with her sister, Jamie, said her sister will accompany the 54th orphan.
"The children are incredible. They're doing so great. I was more upset at the airplane ride than any of them," said McMutrie, who also was at the briefing.
Most of the children's adoption cases were at the end of the bureaucratic process before the 7.0-magnitude earthquake struck.
According to Rendell, adoption cases are under way for 47 of the children. Of these, 40 will be U.S. adoptions, four children will go to Spain and three to Canada. Adoptive parents will be sought for the remaining seven children.
The orphans almost stayed in Haiti.
Rep. Jason Altmire, D-Pennsylvania, who was traveling with the group, said it had been understood that all the children were cleared to leave. However, 14 of them had no papers because they were destroyed in the quake, and the U.S. Embassy said they couldn't leave the country, Altmire said.
"We were frantically calling the State Department, the White House and everyone else" to get the clearance, he said.
In addition, the McMutrie sisters, who live in Altmire's congressional district, refused to allow just a portion of the children to leave, Altmire said.
"So now, everything is up in the air. You're just arguing about paperwork," the congressman said.
Finally, with intervention from several agencies and the White House, the embassy approved humanitarian waivers, or paroles, for the 14 children.
"All of a sudden, after four or five hours of struggle, we got the go that all 54 orphans could come to the U.S.," Rendell said.
By then, the plane that was to take everyone to the United States had left. The military and embassy arranged for them to fly in a military cargo plane.
Altmire said that despite their trauma, the children adjusted well to the flight.
"They were polite and either slept or were quiet or just played among themselves," he said.
"We are all grateful the kids are here and safe, but this was a very unusual situation," an Obama administration official, who did not want to be identified, told CNN.
"We will continue to grant, in special cases, humanitarian parole for orphans and medical evacuees, but our position is clear that people from Haiti attempting to enter the country illegally will be repatriated."
The children were taken by bus to Children's Hospital of Pittsburgh.
Allegheny County spokesman Kevin Evanto told CNN that the children will be placed in foster homes until details of their adoptions are finalized.
On Monday, the U.S. government said it had eased the requirements for orphaned children from Haiti to enter the United States on a temporary basis.
In a separate statement, the State Department said Monday it is working with the Department of Homeland Security and the Haitian government to process nearly 300 cases of Americans who are waiting to adopt Haitian children. Of those, 200 cases are being accelerated.
At least 24 of those children have left Haiti and have joined their adoptive families since the embassy expedited processing for immigrant visas, said Michele Bond, deputy assistant secretary for American citizen services.
Janet Napolitano, secretary of homeland security, can allow otherwise inadmissible people into the country for urgent humanitarian reasons or other emergencies.
Before the earthquake, Haiti was home to about 380,000 orphans, according to the most recent data from the United Nations Children's Fund.
Rendell's plane flew into Haiti on Monday with a shipment of medical aid and several doctors. It arrived after aid organizations had complained that their planes bound for Port-au-Prince had been delayed.
The agency Doctors Without Borders says several of its flights were delayed or diverted for long spells, including a plane carrying supplies for an inflatable hospital. That plane could not land in Port-au-Prince on Saturday and instead was rerouted to the neighboring Dominican Republic, it said. Another medical supply flight was diverted to the Dominican Republic on Sunday, causing a 24-hour delay in delivering aid that had to be transported by truck as a result, the group said.
U.S. officials have attributed the delays to a crowded apron at Port-au-Prince's small airport, but say traffic conditions have considerably improved.
The airport handled 180 flights Monday, none of which were delayed, Lt. Gen. P. K. Keen told CNN. One Doctors Without Borders flight was unable to land over the weekend, he said, because another aircraft's departure was delayed. Instead of circling and burning fuel, the plane landed in the Dominican Republic, he said.
"And clearly, we wanted that field hospital on the tarmac," Keen said. "But beyond landing them on the main runway and shutting down the entire airport for a couple of hours, there weren't many options because of the design of the airfield."
Keen added that planes turned back "a number of times" and "quite a bit" in the first few days after the quake. While the field manages more than 100 flights a day now, before the quake, it handled slightly more than a dozen a day, he said.
CNN's Gary Tuchman, Adam Levine and Mary Snow contributed to this report.