The protests come more than a week after demonstrations in Charlottesville, Virginia, where clashes between white supremacists and counter-protestors turned violent and resulted in one death. Trump drew widespread condemnation for his response to the clashes, in which he blamed "both sides" for the violence.
A police helicopter circled overhead crowds of protesters, telling them to leave the area. Other officers on the ground urged remaining protesters to disperse or be arrested for unlawful assembly, CNN reported.
"People in the crowd began fighting and throwing rocks and bottles at police," Sgt. Jonathan Howard, of the Phoenix Police Department, said in a statement to CNN. "They also dispersed some gas in the area. Police have responded with pepper balls and oc spray in an attempt to disperse the crowd and stop the assaults."
As Trump supporters began trickling in to the convention center, protesters continued to descend upon Downtown Phoenix carrying protest essentials -- signs, megaphones and water bottles to stay hydrated in the 100-plus degree weather.
Carol McGovern wore purple to honor the memory of Heather Heyer, who died while counter protesting in Charlottesville. McGovern came with her daughter, her friend and her friend's daughter.
"We're here for her," McGovern, a Phoenix resident, told CNN. "I can't even imagine being Heather's mother and lost her the way she did when she was coming out just like we are today just trying to be a positive force. This is not a time to be silent...you only send a message if we are in big numbers like this."
Meanwhile, hundreds of other protesters climbed the stairs of the parking lot across the street from the convention center to watch the crowds from higher up.
Joseph Dick, a 34-year-old Phoenix resident, was among those on the roof of the parking lot.
"I definitely expected it was going to be big," Dick, who also participated in the Women's March in Phoenix, said of the anti-Trump protesters. "Usually in Phoenix there's not a lot of movement toward activism but recently it's trending. I think people are really trying to turn the state blue...it's important to show up and represent."