In the latest attempt to disrupt the campaign of the billionaire businessman, protesters in Fountain Hills, Arizona, shut down traffic heading to a planned Trump rally on Saturday.
Protesters, who were shouting slogans and carrying signs as well as flags against Trump, lined themselves up on the main road leading to the rally.
Police arrested a number of demonstrators, but there were no reports of violent clashes.
In New York, demonstrators gathered at Manhattan's Columbus Circle, near one of Trump’s luxury buildings overlooking Central Park.
"Donald Trump, go away, racist, sexist, anti-gay," they shouted.
Protesters held up signs on which were written "Deport Trump" and "Build a wall around Trump."
Some placards read "Don't let bigotry Trump our constitution" and "Will trade 1 Donald Trump for 25,000 refugees."
Trump, who has never held elected office, is leading the race despite the fact that his campaign has been marked by controversial statements, including disparaging remarks about women, Mexican immigrants and Muslims.
Trump says he would deport 11 million undocumented workers from the United States and would establish a "deportation force" for this purpose.
He has also promised to expel undocumented immigrants and build a wall on the US-Mexico border. In addition, he has proposed repealing the constitutional right to citizenship of anyone born on US soil.
Trump has also created a furor in the US and around the world by proposing a "total and complete shutdown of Muslims" entering the United States, following a mass shooting in California.
The New York real-estate mogul has also called for a database to track Muslims across the United States, and he has also said that the US would have "absolutely no choice" but to close down mosques.
Over the past several days, Trump’s rallies have descended into violence between supporters and protesters, and have become heavily secured events teeming with dozens and in some cases hundreds of police.
Trump "is racist, he is sexist, he is homophobic, he is Islamophobic, xenophobic, he is a fascist. It has serious implication for the future of America," said Patrick Waldo, a historian and activist who attended Saturday’s demonstration in New York.
"If we start closing our borders to some people based on their religious beliefs, that is completely unconstitutional ... we start going to a World War II Germany kind of situation and I don't want that in my country," the 31-year-old told AFP.
"Everything he says is racist, is false. It hurts my feelings," said Nour Hapatsha, a 22-year-old Muslim born in America.
Trump blames Clinton
Meanwhile, Trump accused leading Democratic candidate Hillary Clinton of sending her supporters to disrupt his rallies.
Speaking at a rally in Tucson, Arizona, later on Saturday, the billionaire said the protests were "disgraceful," and thanked police for confronting them.
"They arrested three people and everybody else left... They left!" Trump said amid cheers from the crowd.
"I love our police, but we should do a little bit more of that, you'd have a lot less protesters, you'd have a lot less agitators," said Trump.