Democratic presidential candidate Beto O’Rourke greets voters after finishing the Lucky Run 5K race March 16 in North Liberty, Iowa. (Chip Somodevilla/Getty Images)

The Republican National Committee on Sunday sent out a tweet linking Democratic 2020 presidential candidate Beto O’Rourke’s Irish heritage to his 1998 drunken-driving arrest, in an attack that Democrats and some Republicans criticized as being based on stereotypes.

Republicans have previously sought to focus attention on O’Rourke’s DWI arrest, but the tweet by the RNC — which came on St. Patrick’s Day and described O’Rourke as a “noted Irishman” — appeared to be the first time they have raised the topic of his ancestry.

“On this St. Paddy’s Day, a special message from noted Irishman Robert Francis O’Rourke,” the tweet states. It includes O’Rourke’s 1998 mug shot with a leprechaun hat on top, along with the message “Please drink responsibly.”

Speaking with reporters in Milwaukee on Sunday, O’Rourke responded by saying he has attended roughly two dozen campaign events since launching his candidacy and has not once been asked about the arrest.

He argued that voters want to focus on “the big picture, on our goals” and not on “personal attacks.”

The RNC did not immediately respond to a request for comment.

The tweet quickly triggered a backlash, with some Republicans joining Democrats in condemning the message.

“Do better, @GOP,” tweeted Rep. Justin Amash, a libertarian-leaning Republican from Michigan who is often at odds with his party. “Be better.”

Doug Stafford, a top aide to Sen. Rand Paul (R-Ky.), also denounced the tweet, writing, “If you think you’re funny or clever by stereotyping and making fun of any race or nationality to score political points, you’re an idiot, and you should probably not tweet.”

John Weaver, a Republican strategist who worked on the 2016 presidential campaign of Ohio Gov. John Kasich (R), called the tweet “vile” and “indicative of the bottom feeding” Republican Party led by President Trump and RNC Chairwoman Ronna McDaniel.

“With Irish family members, as an American and a world citizen, this is an attack on all races,” he said.

Robert Schmuhl, professor emeritus of American studies at the University of Notre Dame, said the tweet appeared to be an effort by the RNC “to try to neutralize the charisma of O’Rourke by using his formal name and Irish stereotypes.”

“There’s a long, tortured heritage, if you look at the way the Irish were depicted in the 19th century, in newspapers. There, you had depictions of them as rum-loving individuals who were creating havoc in America. To a certain extent, the message about O’Rourke draws on that questionable past,” said Schmuhl, who has studied portrayals of the Irish in America and is the author of the forthcoming book “The Glory and the Burden: The American Presidency from FDR to Trump.”

Schmuhl added that the RNC’s tweet, combined with Trump’s frequent use of the derisive nickname “Pocahontas” for Sen. Elizabeth Warren (D-Mass.), raises questions about how the Republican Party is approaching its messaging against 2020 contenders more broadly.

“Is the party engaging in the use of stereotypes to wound potential opponents?” Schmuhl asked.

Even before announcing his 2020 White House bid on Thursday, O’Rourke, a former congressman who narrowly lost last year in his bid to unseat Sen. Ted Cruz (R-Tex.), had drawn considerable attention from across the aisle: The day before his campaign launch, the conservative Club for Growth released an ad focusing on O’Rourke’s family wealth and accusing him of being “entitled.”

Trump responded Thursday to O’Rourke’s announcement by poking fun at his body language. “I think he’s got a lot of hand movement,” the president told reporters at the White House. “I said, ‘Is he crazy, or is that just the way he acts?’ ”

O’Rourke has called his DWI “a serious mistake for which there is no excuse.” His arrest has long been publicly known, but reports surfaced last summer suggesting that the episode was more serious than detailed in previous media accounts.

State and local police reports said O’Rourke, who was 26 at the time, was driving while drunk at what a witness called “a high rate of speed” in a 75 mph zone of an interstate when he lost control of his Volvo and hit a truck.

O’Rourke “attempted to leave the scene,” according to a witness, and was arrested and charged with DWI. He later completed a court-approved diversion program, and the charges were dismissed.

O’Rourke was also arrested in 1995 for trespassing after he snuck through a fence at the University of Texas at El Paso. The charges were later dropped.

O’Rourke brought up both arrests during his Sunday afternoon campaign stop in Milwaukee, where he talked with a diverse group of Democratic women who are thinking about running for office. He said such mistakes should not hold people back from running for office, as long as they own up to them.

He also acknowledged that “as a white man,” those arrests did not derail his life, as often happens to people of color — a sentiment that prompted many women in the room to snap their fingers in agreement.

“There’s never going to be a perfect candidate or a perfect set of conditions or a perfect time. . . . Don’t let a mistake or something that doesn’t seem to fit the profile of that perfect candidate stop you from running. This democracy needs more, not fewer, of us running for office,” O’Rourke said.

Jenna Johnson in Milwaukee and John Wagner in Washington contributed to this report.