De Niro introduced a performance by Bruce Springsteen – who is also an outspoken critic of the president – by shouting: “It’s no longer Trump, it’s ****ing Trump.”
But the President, who had just returned to the States after meeting North Korean leader Kim Jong-un, countered the star, whose hits include boxing movie Raging Bull.
After seeing a clip of the rant, Mr Trump tweeted: “I watched him last night, and truly believe he may be punch-drunk.
“Robert De Niro, a very Low IQ individual, has received too many shots to the head by real boxers in movies.
“I guess he doesn’t realise the economy is the best it’s ever been with employment at an all time high, and many companies pouring back into our country. Wake up Punchy!”
Meanwhile, Mr Trump yesterday declared that North Korea is no longer a nuclear threat, ignoring critics who accused him of making too many concessions to Mr Kim.
The President tweeted: “Everybody can now feel much safer than the day I took office. There is no longer a nuclear threat from North Korea.
“Meeting with Kim Jong-un was an interesting and very positive experience.
“North Korea has great potential for the future!” The summit, the first between a North Korean leader and a US president, ended with the leaders signing a peace deal.