A Muslim Democrat running for a U.S. House seat in Nevada says that — in a private meeting last year — Senate Minority Leader Harry M. Reid (D-Nev.) had encouraged him to end his campaign by saying, “a Muslim cannot win this race.”

“He said, ‘You should not run for this office,’” said Jesse Sbaih, an immigrant from Jordan who is now a trial lawyer. This race for the House, in a district that includes a swath of suburban Las Vegas, is his first run for political office.

A spokeswoman for Reid, however, denied that Reid had said those words.

Sbaih said it happened after he had entered the House race. He met with Reid in August in a meeting room at the Paris Las Vegas Hotel.

Sbaih said he had sought the meeting in order to win Reid’s support — a key factor in Nevada, where Reid is the unquestioned power broker of Democratic politics. But Reid would not give it, Sbaih said, and cited Sbaih’s religion as one reason why.

“I did not feel that this was an issue. They made it an issue. My campaign is about me being an American,” Sbaih said. He said he had not faced this kind of opposition based on his religion before: “I just turned 40. Been in this country for 29 years. And it’s just absolutely shocking that this occurred.”

A spokeswoman for Reid confirmed that the meeting took place. However, she categorically denied that Reid had cited Sbaih’s religion as a reason he would not succeed.

“Senator Reid did not say that,” said Kristen Orthman, a spokeswoman in Reid’s Senate office. “Jesse Sbaih is a liar and that’s why he is going to lose.”

Sbaih’s assertion could shake up one of the most competitive House races in the country — a race made possible, in a way, by Reid himself.

[Harry Reid, retiring but betting big on Nevada for Democratic Senate majority]

Reid is retiring from the Senate, after 30 years. Rep. Joe Heck (R), who holds the suburban Las Vegas seat now, is running to replace him. That has left the seat open: the Cook Political Report rates it as a “Republican toss-up,” a swing seat vital to both parties.

On the Republican side, several plausible candidates have already filed to run. On the Democratic side, however, the race was slow to start: late in the summer, Sbaih was the best-funded and best-known candidate who had declared.

Sbaih is an ally of Sen. Bernie Sanders (Vt.), who is running, in part, on his own remarkable life story. Sbaih’s parents immigrated from Jordan to Virginia when he was 11, and he helped support the family by washing dishes in an Italian restaurant as a teen.

Now, Sbaih said, his run for office is a way to repay the country for the way it welcomed his family.

“I’ve always felt: The more America gave me, the more I wanted to give back,” Sbaih said in an interview with The Washington Post.

But, Sbaih said, he was rebuffed when he sought to gain Reid’s support.

First, he said, he met with a political consultant connected to Reid, Rebecca Lambe. At a coffee shop, Sbaih said, Lambe brought up his religion and his Arab heritage: “She said, basically, you’re gonna have a problem winning, as a Muslim, as an Arab.”

Lambe disputed that account in an email message to The Post on Monday.

“It’s not what I said,” Lambe said. “As we would with any candidate, we explored his background, profession, religion, the fact he’d never run before, stance on issues and limited support ...to more fully understand the path and potential attacks from the other side.”

Sbaih said he did not record that meeting with Lambe, or the one he had with Reid a few weeks later.

To bolster his account, Sbaih supplied both emails and text messages from the time, in which he tells another Reid ally that he is “profoundly disheartened and saddened that the Democratic Party is refusing to accept a candidate like me because of my religion and ethnicity.”

In the exchanges of text message and emails provided by Sbaih, however, Reid’s allies do not say explicitly that Sbaih’s race or religion is a hindrance, nor do they confirm that Reid himself had said so.

Orthman, Reid’s spokeswoman, said that Reid had told Sbaih he should run for another office — instead of jumping straight into a highly competitive House race.

“We never said he shouldn’t run for elected office. It was that, to run for a congressional seat, your first time, you’re going to lose. And you need more experience,” said Orthman.

Both sides agree that Sbaih pressed on, continuing his campaign for the House.

A few weeks later, Sbaih said, an aide in Reid’s Senate office offered him a chance to apply for a position on the Election Assistance Commission — a federal job. Sbaih said he declined.

Sbaih is still in the House race, but now is facing competition from another Democrat: Jacky Rosen. Rosen, the president of a Las Vegas-area synagogue, is also making her first run for office.

She was recruited by Reid himself, according to Jon Ralston, Nevada’s best-known political reporter.

“She’s been a community leader for years here,” Orthman said, explaining why Reid had recruited a political novice, after criticizing Sbaih for his own lack of experience. “Jesse’s new to the scene.”