"We will accept anyone on humanitarian reasons that needs to come here," acting Commissioner Mark Morgan said during a news conference at the White House. "If your life is in jeopardy and you're in the Bahamas and you want to get to the United States, you're going to be allowed to come to the United States, whether you have travel documents or not."
"We have to be very careful. Everybody needs totally proper documentation because, look, the Bahamas had some tremendous problems with people going to the Bahamas that weren't supposed to be there," Trump told reporters on the South Lawn of the White House before embarking on a trip to North Carolina, where he planned to tour areas hard hit by Dorian.
"I don't want to allow people that weren't supposed to be in the Bahamas to come into the United States, including some very bad people and some very bad gang members, and some very, very bad drug dealers. So, we're going to be very strong on that."
"Please, all passengers that don’t have a U.S. visa, please proceed to disembark," a crew member said over a loudspeaker, according to a cellphone video obtained by Miami TV station WSVN.
"At the last minute like this, it’s kind of disappointing," Renard Oliver, one of the evacuees who disembarked with his baby daughter, told WSVN. "It’s hurtful because I’m watching my daughter cry, but it is what it is."
Morgan acknowledged there was "confusion," but appeared to lay the blame on the ferry operator.
"We're not ... telling the cruise line that you cannot allow anyone without documents. That's just not being done," Morgan said.
In an earlier statement Monday, CBP officials said that once they learned the vessel was "preparing to embark with an unknown number of passengers" in Freeport, a city on Grand Bahama Island, they reached out to the ferry operator and requested they coordinate with the U.S. and Bahamian government in Nassau before departing the Bahamas.
"Everyone who arrived to the United States from another country must present themselves to a CBP officer for inspection at an official CBP Port of Entry," the statement reads. "All persons must possess a valid identity and travel documents."
ABC News reached out to the ferry operator for comment, but had not heard back.
During his news conference, Morgan said CBP officials processed about 1,400 people in a couple of hours over the weekend after they were evacuated to Palm Beach, Florida, on a cruise ship.
Morgan said CBP is not processing people "with a blind eye."
"But keep in mind, there are still people that are inadmissible to this country, there are still people coming here who still could have criminal convictions," he said. "We are going to process them and handle them normally to make sure this country is safe."
He said the Trump administration is also considering granting Temporary Protected Status to some evacuees of the Bahamas.
"I think that would be appropriate to have that circumstance," Morgan said. "History shows we've done that before. So if history shows that it's taken a long time to get the Bahamas back to where the people can return, I'm sure that will be a discussion that we'll be having."
Dorian slammed the Bahamas on Sept. 2, blowing ashore as a monster Category 5 hurricane, tying the record for the strongest Atlantic hurricane ever to make landfall.
The hurricane killed at least 50 people, but Bahamian government officials said the death toll is likely to grow dramatically as search crews comb hundreds of wrecked homes in search for bodies. Bahamian Health Minister Dr. Duane Sands told ABC News on Sunday that it is possible some victims were washed out to sea and may never be found.
The hurricane left about 76,000 people homeless and in need of assistance in the Abaco Islands and Grand Bahama Island, according to the United Nations.
Bahamas Power and Light Company said on Monday that the power grid on the Abaco Islands was totally destroyed and will have to be completely rebuilt.
"There are no standing electricity poles along the 16-mile stretch from Marsh Harbour to Treasure Cay" in the Abaco Islands, according to the power company's statement. "Our infrastructure along that stretch has been obliterated."
The agency went on the say that a primary concern of the reconstruction effort will be housing people displaced by the hurricane.
"There is nothing left standing in the Central and North Abaco that can house the numbers of people required to do the work," the statement reads.
Massive amounts of drinking water and other supplies continue to pour into the island nation, much of it from the United States.
John Michael-Clark, co-chairman of the Disaster Relief and Reconstruction Committee in the Bahamas, said two relief centers are being established in hard-hit Marsh Harbour to help people rebuild their homes immediately. He estimated the relief centers could house around 4,000 people.
But Michael-Clark warned the reconstruction effort will be long.
"These could be there anywhere from 180 days and 365 days depending on what happens in our assessments," he said.
ABC News Marcus Moore and Brandon Baur contributed to this report.