HUDSON, N.H. — US Senator Ted Cruz, under sustained attack from Donald Trump over whether he is eligible for the presidency, offered perhaps his most pointed response Tuesday, dismissing the legal questions and arguing the Republican front-runner is playing into Democrats’ hands.

On Monday, Trump cited Harvard Law professor Laurence Tribe to doubt whether Cruz, who was born in Canada to parents who were US residents, is constitutionally qualified for the White House. After a Second Amendment rally on Tuesday, Cruz told reporters the questions were “straightforward’’ and settled.

The Texas Republican, who has overtaken Trump in some polls of the Iowa caucuses, said Democrats were fueling Trump’s attacks because he is the preferred opponent of Democrat Hillary Clinton. Trump is the GOP’s dominant front-runner in surveys of the Feb. 9 primary in New Hampshire, although Cruz has recently increased his efforts in the state with additional staff.

“It is more than a little strange to see Donald relying on as authoritative a liberal, left-wing judicial activist Harvard Law professor who is a huge Hillary supporter,’’ Cruz said. “It starts to make you think. ‘Gosh, why are some of Hillary’s strongest supporters backing Donald Trump?’ ’’

Standing in a small room inside a shooting range and gun shop, and facing a bank of cameras, Cruz continued: “You know, the last couple of elections, you’ll recall, the Democrats got the nominee they wanted to run against in the general election. It seems the Hillary folks are very eager to support Donald Trump and the attacks that are being tossed in my direction.’’

Cruz had sought to tamp down the negative impact of Trump’s attacks for most of this month, either brushing them off when asked directly about them or playfully responding via social media. The two are jockeying for the hearts of the GOP’s energetic conservative base, and until the eligibility critiques, Cruz had largely sailed through the primary without facing blasts from Trump like those that have withered other candidates.

At a Monday-morning rally in Windham, Trump continued to hammer the eligibility issue. Many scholars have maintained that Cruz qualifies as a natural-born citizen under the constitutional criteria, though Tribe, who was Cruz’s law professor at Harvard, has disagreed.

“It is not a settled matter,’’ Trump said Monday. “You can’t have a nominee who will be subject to not being the nominee.’’

That charge made it inevitable that Cruz would have to answer questions when he arrived in New Hampshire Tuesday, though his express purpose was to headline an outdoor Second Amendment event, during which he criticized President Obama and Clinton.

A group of Republicans from outside the party’s moderate establishment spoke before Cruz, including Bob Smith, a former US senator from New Hampshire, and the former state House speaker Bill O’Brien.

With a mammoth American flag as his backdrop, a barn-jacketed Cruz took the stage after former US congressman Bob Barr of Georgia, but Cruz was quickly interrupted by a young man in a suit, who questioned from the stage why hundreds of people had gathered in support of guns.

Cruz encouraged the man to leave the stage, then joked, “Did he not get the memo? It’s ‘live free or die.’ It’s not ‘live coddled by a bunch of nanny-state liberals or die.’?’’

After a second young man was hustled away from the stage when he interrupted, Cruz said, “What is it about freedom that’s so terrifying to liberals?’’

Cruz said he had awakened early Monday morning “to go sit in a duck blind and blow some ducks out of the air. That’s a wonderful thing.’’ But, he said, the Second Amendment is less about hunting and skeet shooting than about family protection and fundamental freedoms.

“The Second Amendment is a check on tyranny,’’ Cruz said.

Ron Trombley of Hudson, who stood in the cold outside the Granite State Indoor Range, said the only gun he owns is a Japanese rifle from World War II, but that he liked what he heard from Cruz.

“He’s a constitutionalist,’’ Trombley said, who could help resolve “the blockage’’ in Washington.

Cruz said he planned to skip Obama’s State of the Union address Tuesday night but told reporters that he expected the president to attain “heights of demagoguery’’ that he had not yet reached.

Cruz, who was making his first appearance in the state in about two months, is due back in New Hampshire for an extended stay next week, with five days of events planned around the state.

Jim O’Sullivan can be reached at jim.osullivan@globe.com. Follow him on Twitter at @JOSreports.