The 46th US President made the comments during his first official White House press conference since his inauguration on January 20, 2021.
President Biden was responding to a question from a journalist about the current situation with people trying to enter the United States at its border with Mexico.
The journalist said she had spoken to two young children under the age of 10 at the border the day before Thursday's press conference.
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The mother of one of the children spoke to the journalist on a phone telling her the reason she had sent her children unaccompanied to the Mexico-USA border was because she believed President Biden was a "good man" and would grant her children sanctuary in America.
President Biden responded by saying that any parent who makes such a decision would not do so likely and suggested the reason it was happening was because people feel they have no other options available to them.
To explain why he believes people like those along the Mexico-USA border take great risks to reach a country like America, President Biden referred to his own Irish ancestors leaving Ireland for America at the time of the Great Famine of the 19th century.
"People in Guadalope saying, 'I have a great idea, let's sell everything we have, give it to a 'Coyote', have him take our kids across the border into the desert where they don't speak the language, won't that be fun, let's go' - that's not how it happens, people don't want to leave.
"When my great-grandfather got on a coffin ship in the Irish Sea, expectation was, was he going to live long enough on that ship to get to the United States of America?
"But they left because of what the Brits had been doing - they were in real, real trouble, they didn't want to leave but they had no choice.
"I can't guarantee we will solve everything but I can guarantee we can make everything better," said President Biden.