Former President Donald Trump continues to push a false claim that Democrats can vote in Tuesday's New Hampshire's GOP primary and "infiltrate" the process.

       "Independents and Democrats are allowed to vote, so in order to try and stop Trump, they go out and they sign up and they can sign up very easily," Trump said Thursday during an appearance on Fox News' "Hannity," a claim he's made repeatedly in recent days. "And so somebody should have stopped it."

       New Hampshire is an open primary and independents can legally participate in either the Republican or Democratic primaries.

       Registered Democrats are allowed to vote only in a Democratic primary. The cutoff for voters to change their party affiliation was in October.

       Republican presidential candidate former U.S. President Donald Trump looks at supporters as he arrives at a campaign event, Jan. 17, 2024, in Portsmouth, N.H.

       Timothy A. Clary/AFP via Getty Images

       MORE: Fresh off Iowa win, Trump sets sights on battling Haley in New Hampshire

       Trump's comments come as GOP candidate Nikki Haley and her surrogate, New Hampshire GOP Gov. Chris Sununu, have advocated for independent voters, not registered Democrats, to participate in the GOP primary process as Haley attempts to court them in order to cut into Trump's commanding lead in the state.

       Trump has also attacked Sununu, accusing him of allowing election "fraud" in the state, and claiming he should've done more to change the state's storied primary process.

       "Governor Chris Sununu … should spend more time keeping Democrats from voting in the Republican Primary," Trump wrote on his social media platform on Friday.

       He's been repeating the claim in recent days as polls showed Haley gaining ground on him in New Hampshire.

       The Trump campaign doubled down on his rhetoric, with spokesman Steven Cheung telling ABC News, "President Trump is absolutely correct when he says Nikki Haley is relying on liberals and Democrats to infiltrate because that's who she appeals to," claiming thousand of Democrats had switched to undeclared before the cut-off date.

       Republican presidential candidate former UN Ambassador Nikki Haley talks to students, parents and educators during a campaign stop at the Polaris Charter School, Jan. 19, 2024, in Manchester, N.H.

       Charles Krupa/AP

       MORE: Sununu lowers expectations for Haley in Tuesday's New Hampshire GOP primary

       The system is the same as it it was in the 2016 primaries, when Trump won New Hampshire by nearly 20 points.

       As Trump continues to lead in New Hampshire primary polls, according to 538's polling average, Haley has focused on undeclared voters.

       Over 40% of registered undeclared voters in the state are able to vote in the Republican or Democrat primaries. In 2024, it's expected some will choose to vote in the competitive Republican contest given that President Joe Biden's name will not be on the Democratic ballot.

       In response to Trump's claims, Haley wrote on X that Trump's falsehood was just the latest example of why "we need to move on from Trump: too many lies."

       "Democrats can't vote in the NH primary. They haven't been able to change their registration for months," Haley continued in her post.

       Trump in recent days has been attempting to paint Haley as a Democrat or candidate backed by Democrats, accusing her of accepting donations from donors that have given to Democrats in the past, claiming she "sided with Biden" to oppose Trump's immigration policies, and even posting on social media a photo of Hillary Clinton with a Haley's face.

       "A vote for Nikki Haley this Tuesday is a vote for Joe Biden and a Democrat Congress, because that's what's gonna happen," Trump said at a campaign event in Portsmouth, New Hampshire, on Wednesday.

       MORE: Trump tops his opponents while Biden hits a new low in approval ahead of Iowa caucus: POLL

       Calling claims that Democrats are trying to infiltrate the Republican primary "irresponsible," Haley defended her record as a conservative Republican.

       "How am I not conservative?" Haley said on Fox News. "I was a tea party governor, I passed voter ID, I passed the toughest illegal immigration law in the country, I cut taxes, I passed tort reform, we paid down our debt, I went to the U.N., we cut a billion dollars."

       "There are multiple instances that we need to start asking Donald Trump the questions and stop taking what he's saying to be golden," she said..