Speaking in the Oval Office alongside Irish premier Leo Varadkar, Mr Trump said Brexit was “tearing a lot of countries apart”.
The president, who earlier set out his hopes for a “large scale” US-UK trade deal, added that “I’m not sure anybody knows” what was happening with Brexit.
Mr Trump was speaking in the Oval Office after greeting Mr Varadkar.
“It’s a very complex thing right now, it’s tearing a country apart, it’s actually tearing a lot of countries apart and it’s a shame it has to be that way but I think we will stay right in our lane,” Mr Trump said.
The US president again claimed Theresa May had ignored his advice on how to handle the talks.
The Prime Minister has previously revealed that Mr Trump told her to “sue the EU” and “not go into negotiations”.
Mr Trump said: “I’m surprised at how badly it’s all gone from the standpoint of a negotiation. I gave the Prime Minister my ideas on how to negotiate it and I think you would have been successful.
“She didn’t listen to that and that’s fine - she’s got to do what she’s got to do.
“I think it could have been negotiated in a different manner, frankly. I hate to see everything being ripped apart now.”
On the prospect of another referendum, he said: “I don’t think another vote would be possible because it would be very unfair to the people that won. They’d say ‘What do you mean, you’re going to take another vote?’ So that would be tough.
“I thought it would happen, it did happen, and both sides are very, very cemented in. It’s a tough situation. It’s a shame.
“There was no reason for that to happen. They could have had the vote and it should have gone smoothly and unfortunately it didn’t.”
With MPs considering seeking to extend Article 50, the US president said Brexit was likely to be delayed.
“I think they are probably going to have to do something because right now they are in the midst of a very short period of time - the end of the month - and they are not going to be able to do that.”
Mr Trump said he would like to see the “whole situation with Brexit work out”, adding “we are talking with them about trade and we can do a very big trade deal with the UK”.
Turning to Mr Varadkar, he said: “Leo, I’m sure you agree on that. Would you like to express your feelings on Brexit? Maybe I shouldn’t let you do it, I’ll just get you in trouble.”
Mr Varadkar replied: “We have a different opinion, Mr President. I regret that Brexit’s happening.”