the candidate outlined his plans to combat Islamic extremism, including a new screening test for arrivals to the US.
Applicants will be tested to determine if they share Western liberal values like LGBT and religious tolerance.
Democratic rival Hillary Clinton poured scorn on his plan, labelling it a "cynical ploy".
"This so-called 'policy' cannot be taken seriously," said her spokesman.
"How can Trump put this forward with a straight face when he opposes marriage equality and selected as his running mate the man [Mike Pence] who signed an anti-LGBT law in Indiana?"
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Under Mr Trump's plan, citizens from countries with a history of terror will be banned but it is not clear which nations.
In the speech, he did not lay out his own military strategy for defeating the so-called Islamic State.
But he did repeat his claim he was opposed to the Iraq War before it began, which fact-checkers say is untrue.
And he said that the oil in Iraq should have been seized by the US government to prevent it from becoming the property of IS.
In his speech, Mr Trump promised to:
Ban immigration from countries where terrorism is widespread and vetting is poor
Make alliances with all countries fighting against terrorism
Introduce an ideology test for new immigrants arriving to the US
Keep Guantanamo Bay prison open
Establish a presidential commission to investigate Islamic terror
Work with Nato, despite previously calling it "obsolete"
The billionaire initially proposed a blanket ban on all Muslims but has changed it to one that is based on an unspecified list of countries that export terror.
The latest proposal includes creating an ideological test for immigrants entering the country, with questions addressing how each applicant views American values such as religious freedom, gender equality and gay rights.
"Those who do not believe in our Constitution, or who support bigotry and hatred, will not be admitted for immigration into the country," he said.
Analysis: Jonathan Marcus, BBC Defence and Diplomatic Correspondent
It was a speech organised largely around one theme - the threat from radical Islam. So paradoxically, it was in this sense firmly within the existing US foreign policy mainstream.
This mainstream has elevated the threat from groups like so-called Islamic State and al-Qaeda into a phenomenon that requires nothing short of a "war against terror" in response.
The title of Mr Trump's speech referred to "the Age of Terror" no less.
As for other major "threats" to America's position in the world - a rising China, a more belligerent Russia, America's own failing economic competitiveness, or the cohesion of its own society - there was no mention.
Mr Trump was clear. His America would defeat "radical Islamic terrorism". And he repeated his assertion that the rise of self-styled Islamic State (Isis as he called it) was a direct result of the policy decisions made by President Barack Obama and his one-time Secretary of State Hillary Clinton.
Mr Trump said that the test will not only expose terrorist sympathisers, but also will "screen out any who have hostile attitudes towards our country or its principles".
He heavily criticised his rival Hillary Clinton, saying that she lacks the "mental and physical stamina" to defeat IS.
And he attacked her plan to increase the rate of Syrian refugees arrivals, which he claimed would cost $400bn (£315bn).
Mr Trump is still facing a backlash for repeatedly describing Mr Obama and his Democratic rival for the White House, Hillary Clinton, as "founders" of Islamic State.
Vice President Joe Biden speaking at a campaign event with Hillary Clinton said that Mr Trump's claim that Mr Obama and Mrs Clinton had "founded" IS proved his views to be "dangerous" and "un-American", and that it had made US soldiers in Iraq less safe already.
Recent polls show him significantly trailing Hillary Clinton in key battleground states.
