Donald Trump's hardline stance on immigration after two bombings in the New York area again sparked debate on the White House campaign trail Tuesday, as his son caused a firestorm by comparing Syrian refugees to lethal candies.

The Republican presidential hopeful's uncompromising position on undocumented migrants -- even calling them a dangerous "Trojan horse" who enter the country with the aim of doing harm -- is inextricably linked to his meteoric political rise.

Most Republicans approve of his tough talk, with polls showing that a majority of party members agreed with his call last December to bar Muslims from entering the United States.

Since then, Trump has refrained from specifically targeting Muslims, but he has championed police profiling of suspects and promised to bar immigrants and travellers from certain countries deemed dangerous, such as Syria.

The candidate has repeatedly warned of the risks posed by Syrian refugees, citing the arrival in Europe of Islamic State operatives disguised as simple refugees, and says US immigration officials are not properly screening new arrivals.

"We want to make sure we are all only admitting people in our country who love our country," he said Tuesday in a speech at High Point University in North Carolina.

"It's just a plain fact that our current immigration system makes no real attempt to determine the views of the people entering our country. We have no idea who they are, what they think," he said.

Trump also denounced the "open borders" that he said his Democratic rival Hillary Clinton advocated as secretary of state, blaming her for the rise of the Islamic State group.

"All these disasters with ISIS happened on Hillary Clinton's watch, happened with her, her bad judgment, her bad decision-making," he said. "Her attacks on me are all meant to deflect from her record of unleashing this monstrous evil upon us."

Immigration is not one of the major issues on the minds of voters, ranking fourth according to a recent CBS/New York Times poll, making it unclear if Trump, 70, can use it to persuade those who are still undecided.

But national security and the anti-terror fight are number two on that list, and with less than 50 days to go before Election Day on November 8, Trump is attempting to blur the lines between the two issues.

- Syrians and Skittles -
Trump's son Donald Jr, one of his surrogates on the campaign trail, has meanwhile courted controversy with a tweet comparing Syrian refugees to a bowl of multi-colored Skittles candy -- some of them lethal, but not to the naked eye.

"This image says it all," he said on Twitter, with a picture of a white bowl filled with the popular sweets.

Written above the image is: "If I had a bowl of skittles and I told you just three would kill you, would you take a handful? That's our Syria refugee problem."

Trump Jr thus argued that it is too dangerous to welcome migrants when a tiny number of them could later launch attacks. The man accused of planting bombs in downtown Manhattan and near a race in New Jersey over the weekend is a naturalized American of Afghan descent.

At his rallies, Trump Sr has repeatedly recited the lyrics to a 1960s song, "The Snake," which recounts how a woman who aided an injured snake ended up being bitten, and he used the Trojan Horse imagery to warn of hidden dangers.

"We cannot let this evil continue. Cannot do it," he said Monday.

"Nor can we let the hateful ideology of radical Islam, its oppression of women, gays, children and non-believers, be allowed to reside or spread within our country."

Wrigley, the maker of Skittles, on Tuesday criticized Trump Jr's tweet.

"Skittles are candy. Refugees are people. We don't feel it's an appropriate analogy," a company statement said.

Trump's Democratic rival Hillary Clinton, who had no public events scheduled on Tuesday a week after taking a break from campaigning to recover from pneumonia, backs President Barack Obama's position on immigration.

Obama has increased the number of Syrian refugees granted entry to the United States in the face of the brutal five-year war in their homeland.

On Tuesday, Clinton used a call with a group of advisors on national security issues to emphasize the need for "experienced, steady leadership" to defeat extremist groups like IS.

"Calm, not panic. Resolve, not fear," she said in remarks released by her campaign.

"We can't lose our cool and start ranting and waving our arms. We shouldn't toss around extreme proposals that won't be effective and lose sight of who we are. That's what the terrorists are aiming for," she said.

Meanwhile, former president George H.W. Bush plans to vote for Hillary Clinton in November, the niece of president John F. Kennedy wrote in a Facebook posting.

"The President told me he's voting for Hillary!!" read the caption of a picture Kathleen Kennedy Townsend posted on Facebook, as she shook the 92 year-old ex-president's hand.