EU's chief Brexit negotiator: Donald Trump's brand of American populism came from Europe
Responding to a question about Trump's ban on refugees from seven majority-Muslim countries, Verhofstadt said that the president's views and policies came from populists in Europe.
"Populism by Trump is more influenced by our populism than the opposite. It's the opposite of what people think - it's from here first and it went over to the Atlantic," Verhofstadt said.
Anti-immigration populist movements have grown in strength around Europe in the past decade, leading the UK voting to leave the European Union in June and the rise of the 5 Star Movement in Italy and the Marine Le Pen's Front National in France.
Trump on Friday signed an executive order banning people from seven majority Muslim countries - Iraq, Iran, Libya, Somalia, Sudan, Syria, and Yemen - from travelling to the US.
The move has attracted widespread criticism from world leaders and sparked protests across the US.
A petition on Parliament's website calling for US President Donald Trump not to be given a full state visit to the UK has gained more than 1 million signatures in less than 48 hours.
"I have just come back from US and my view is that we have a third front that is undermining the EU ... and that is Donald Trump," said Verhofstadt.
"20 million people have died because of nationalism in Europe. There is not one family living on the continent and certainly also not in Britain who has no grandfather, grandmother, who was not a victim of these stupidities, these atrocities at the end of the 19th and the whole 20th century.
"Putting your future organisation of Europe on nationalist ideas is the most stupid thing you can do. It's playing with fire knowing what it has created in the past."
Verhofstadt also highlighted his own role in the Brexit negotiations. While they will be led by Michel Barnier, the European Commission's chief negotiator, Verhofstadt said that any deal would have to be ratified by the European Parliament as well to be legally enacted.
If EU parliament does not sign off on the deal, the UK "will exit without any agreement," Verhofstadt said.