Two officers were assaulted and suffered "minor bumps and bruises," Cleveland Police Chief Calvin Williams said.
Two people were arrested on felony counts and 15 others on misdemeanor charges.
Protests and US probe after Louisiana police shoot black man
"There are people that don't want to just protest," Williams said.
"Their only reason for being here is disruption, disorder and chaos."
Tensions flared on the street in front of a secure entrance area to the Quicken Loans Arena, where Republicans anointed Donald Trump as their party's 2016 presidential nominee.
A protester tried to set an American flag on fire, and in the process caught his pant leg on fire. A police officer responded to put the flames out, and the protester punched and pushed the officer, Williams said.
In the skirmish, the pant legs of two other people nearby also caught on fire, the chief said.
Security forces, including horse-mounted police, closed ranks around the protesters, and detained people were seen kneeling with their hands behind their backs.
A group calling itself the Revolution Club sent out a press release earlier saying that Joey Johnson, a "notorious flag burner and revolutionary communist," would conduct civil disobedience in Cleveland.
Police declined to identify the arrestees, because they had not yet been booked and officially charged, but a member of the group said that Johnson was among those arrested.
A woman from the same group also was seen trying to burn a second flag. Police intervened and tussled with protesters as an officer snatched away the singed flag.
Later, the woman was arrested, as people chanted "Let her go!"
Protests over shootings block roads in US cities, arrests made
Demonstrations have taken place mostly peacefully in the city during the week of the convention, although scuffles have broken out during some protests.
The police chief emphasized that there have only been 22 arrests over the three days of the convention.
"So far so good," Williams said, "We're still out there. We're still vigilant."
Police have been on alert in the Ohio city, and security was ramped up dramatically for the week of the Republican convention in the wake of the recent killings of police officers in Dallas, Texas and Baton Rouge, Louisiana.
COMMENTS (1)
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ