Donald Trump has called for "extreme vetting" of immigrants and pledged to make dramatic changes to US immigration policy if he wins the presidential race in November.

In a speech in the swing state of Ohio on Monday, Trump said he would develop a screening test to combat the threat of Islamic extremism.

Having previously called for a temporary ban on Muslim immigrants to the US – a move which has been widely criticised as Islamophobic – Trump said that applicants would be tested on whether they "share our values and respect our people".

"In the Cold War, we had an ideological screening test. The time is long overdue to develop a new screening test for the threats we face today," the Republican candidate said. "I call it extreme vetting. I call it extreme, extreme vetting."

The Clinton campaign criticised Trump's suggestion, branding it "a cynical ploy to escape scrutiny of his outrageous proposal to ban an entire religion from our country and no one should fall for it."

"How can Trump put this forward with a straight face when he opposes marriage equality and selected as his running mate the man who signed an anti-LGBT law in Indiana?" Hillary Clinton's senior policy adviser Jake Sullivan said.

Trump's speech roundly condemned "the hateful ideology of radical Islam" and said its "oppression of women, gays, children, and nonbelievers [must not] be allowed to reside or spread within our own countries.

"We will defeat radical Islamic terrorism, just as we have defeated every threat we have faced in every age before. But we will not defeat it with closed eyes, or silenced voices," he said.

"In addition to screening out all members or sympathisers of terrorist groups, we must also screen out any who have hostile attitudes towards our country or its principles – or who believe that Sharia law should supplant American law.

"Those who do not believe in our Constitution, or who support bigotry and hatred, will not be admitted for immigration into the country.

"Only those who we expect to flourish in our country – and to embrace a tolerant American society – should be issued immigrant visas."

Trump repeated his pledge to "temporarily suspend immigration from some of the most dangerous and volatile regions of the world that have a history of exporting terrorism" and said he would stop processing visas from countries where "adequate screening cannot take place... until such time as it is deemed safe to resume based on new circumstances or new procedures."

He criticised Clinton's proposed immigration policy, saying the Democrat candidate "wants to increase the flow of Syrian refugees by 550 per cent".

"Hillary Clinton wants to be America's Angela Merkel, and you know what a disaster this massive immigration has been to Germany and the people of Germany – crime has risen to levels that no one thought would they would ever see. We have enough problems in our country, we don't need another one," Trump said.

"This is my pledge to the American people: as your President I will be your greatest champion. I will fight to ensure that every American is treated equally, protected equally, and honoured equally. We will reject bigotry and oppression in all its forms, and seek a new future built on our common culture and values as one American people.

"Only this way, will we make America Great Again and Safe Again – for everyone."