Instead of unifying a politically divided nation, the worst terror attack in the United States since September 11, 2001 has widened the gap between the White House contenders over how to tackle extremism and keep Americans safe.

Both candidates used their speeches in the wake of the shooting to enhance their commander-in-chief credibility, in starkly different tones.

Presumptive Republican nominee Trump ratcheted up his pointed rhetoric, blasting Clinton for seeking to "allow radical Islamic terrorists to pour into our country" and suggesting the former secretary of state "has no clue" about radical Islam.

"When I''m elected, I will suspend immigration from areas of the world where there is a proven history of terrorism against the United States, Europe or our allies, until we fully understand how to end these threats," Trump said during a highly-anticipated national security speech in New Hampshire.

"We cannot continue to allow thousands upon thousands of people to pour into our country, many of whom have the same thought process as this savage killer," he said, referring to the Orlando gunman, whom US authorized suspect was radicalized by Islamist propaganda.

The provocative billionaire again called for a halt to Syrian refugees entering the United States and warned there are people living in America with "hate in their heart."

In an exchange with Fox News, Trump said President Barack Obama "doesn''t get it" when it comes to the extremist threat, a comment that drew curt reaction from the White House.

"When you are focused on something as big as helping the country respond to the worst mass shooting in our nation''s history... and combating violent extremism, it''s important not to get distracted by things that are so small," White House spokesman Joshua Earnest said.

- ''Metastasizing'' threat -

Trump heaped criticism on his rival.

"The burden is on Hillary Clinton to tell us why she believes immigration from these dangerous countries should be increased without any effective system" of screening, Trump said.

"She wants to take away Americans'' guns and then admit the very people who want to slaughter us."

Clinton made no mention of Trump in her speech, instead urging Americans to reject political partisanship and "stand together" to defeat terrorism.

"The Orlando terrorist may be dead, but the virus that poisoned his mind remains very much alive and we must attack it with clear eyes, steady hands, unwavering determination and pride in our country and our values," she said.

"The threat is metastasizing."

While Clinton zeroed in on fighting Islamic State extremism and the need to rein in American gun violence, Trump seized on how Muslims may be protecting their own.

"We have to get the people that surround these maniacs to start talking," he told ABC.

Trump''s argument followed his accusations that neighbors and relatives of the San Bernardino attackers who slaughtered 14 people in December knew the couple had been radicalized but did not alert authorities.

Clinton for her part recognized the need to track so-called lone wolves and prevent them from launching attacks, and reiterated her call for reinstatement of an assault weapons ban, saying Orlando shooter Omar Mateen used a "weapon of war" to kill 49 people.

But she stressed that "inflammatory anti-Muslim rhetoric" and bans based on religious affiliation would only hurt the vast majority of Muslims who abhor terrorism.

She warned that demagoguery would not end terrorism.

"I''m not going to demonize and demagogue and declare war on an entire religion," Clinton said.

But she did demand that other governments reconsider policies that allow extremism to thrive, calling out three US allies.

"It is long past time for the Saudis, the Qataris and the Kuwaitis and others to stop their citizens from funding extremist organizations," Clinton warned, urging them to stop supporting "radical schools and mosques" that promote extremism.

Trump expressed strong support for America''s gay community, following Sunday''s attack on the gay nightclub.

"It''s an assault on the ability of free people to live their lives, love who they want and express their identity," he said.

"It''s a strike at the heart and soul of who we are as a nation."