Leo Varadkar also thanked President Trump for his support of a new E3 visa programme which, if passed by Congress, would benefit Irish citizens who wish to work in the US.
"The president, who described Brexit as a" lovely, attractive thing" during a visit to Scotland in June 2016, said the UK's divorce from the European Union is "tearing apart" Britain and other member states which he believes is "a shame".
Trump added: "I'm surprised at how badly it's all gone from the standpoint of a negotiation".
Asked if he thinks the Brexit deadline should be extended, Mr Trump said: "I think they are probably going to have to do something because right now there are in the midst of a very short period of time, at the end of the month and they are not going to be able to do that".
Mr Trump also used Mr Varadkar's visit to the White House yesterday to warn Ireland and the EU the U.S. is "going to tariff a lot of their products coming in because the European Union treats us very, very unfairly".
Mrs Foster has said she hopes to invite Mr Trump to attend the Open Championship at Portrush this July.
"I will be coming at some point this year", he said.
After Brexit, "we can do a very big trade deal with the United Kingdom", noted Trump.
While Varadkar prepared to have breakfast with Pence and a who's who of Irish-Americans, including the president of Notre Dame, Trump tweeted an open invitation to Britain to free itself of the European Union and its trade rules.
The Taoiseach, Leo Varadkar, will travel to Chicago today as part of the annual Saint Patrick's Day programme of events.
The Irish PM said the most pressing issue facing his country was how to settle questions about the future of the border between Ireland, an European Union member, and Northern Ireland, which won't be. "I regret Brexit's happening". "There is every expectation in Washington that a U.S. -U.K. trade deal could be in place by the end of 2019 if Brexit goes forward this month and Britain successfully leaves the Customs Union".
"I predicted it was going to happen, and I was right".
She told BBC News NI that she would "very much" like to se the U.S. president visit Northern Ireland.
"I look forward to talking to you later about Brexit, giving you our perspective on it and the real importance of protecting the Good Friday Agreement and the really hard-won peace in Northern Ireland", Varadkar told Trump, referring to the 1998 British-Irish peace accord.
"We talked about Brexit, something that is turning out to be a little more complex than they thought it would be".
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