The White House on Tuesday re-upped a social media insult depicting top Democrats in sombreros as a way to suggest they are soft on immigration.

The fake image of Representative Hakeem Jeffries of New York and Senator Chuck Schumer of New York was captioned: “Happy Cinco de Mayo to all who celebrate!”

The posting was a reprisal of one that President Trump, who has often used racist attacks against his political opponents, posted in September and which was widely condemned as racist. That post was designed to goad Democratic leaders during negotiations over a government shutdown, and falsely accused them of trying to give free health care to undocumented immigrants.

On Tuesday, Mr. Schumer and Mr. Jeffries hit back with a meme of their own, posting a chummy image of President Trump and Jeffrey Epstein, also with sombreros superimposed on their heads.

“Happy Cinco de Mayo, @WhiteHouse!” the post said.

Davis Ingle, a White House spokesman, responded with an attack on The Times.

Mr. Trump has escalated his attacks on Mr. Jeffries in recent weeks, posting repeatedly about him on his Truth Social platform. He blasted Mr. Jeffries for criticizing the Supreme Court — which Mr. Trump has also repeatedly attacked — after the Democrat called it “illegitimate” for gutting the Voting Rights Act.

Last Friday, Mr. Trump posted a picture of Mr. Jeffries holding a baseball bat, and called him “Low IQ,” an insult Mr. Trump has frequently lobbed at Black people.

“Low IQ Democrat Minority Leader, Hakeem Jeffries, is nothing but a THUG, and he is a danger to our Country!” Mr. Trump wrote.

Mr. Jeffries has hit back at the president in television interviews and social media posts, saying that the president suffered from “Jeffries Derangement Syndrome,” — a twist on the “Trump Derangement Syndrome” the president often cites to attack his critics.

Mr. Jeffries also offered a pointed response to Mr. Trump’s insulting his intellectual ability. “It’s extraordinary to me that Donald Trump keeps recycling this low-IQ insult,” Mr. Jeffries said in a news conference last month. “This is from the dumbest president ever to sit at 1600 Pennsylvania Avenue, and there’s not even a close second.”