Ted Wheeler, Portland's mayor, said he was not concerning himself with tweets from Washington, and he praised the response by law enforcement.
Wheeler later tweeted that, after preparing for the worst, he was relieved "no lives were lost" and weapons were quickly seized.
At least six people suffered minor injuries, according to police.
Members of Antifa line up during an alt-right rally in Portland, Oregon. He added, "Portland is being watched very closely".
Police have arrested 13 people on a range of charges, including disorderly conduct, resisting arrest and unlawful use of a weapon after right-wing demonstrators squared off with Antifa counter-protesters in Portland, Oregon.
Antifa's presence at the event attracted the attention of President Trump, who tweeted that "major consideration" is being given to naming the group an "organization of terror".
"That group of Antifa there in Portland needs to be exposed for who they are", Biggs told the Associated Press Tuesday.
"We know in this political environment, we will be criticized for what we do and what happens, no matter the outcome", Jones said.
Eric K. Ward, executive director of the Portland-based Western States Center, said the right-wing rally was a bust. The weapon in question, as revealed by a longer video, was initially brought to the protest and used by a far-right demonstrator against Antifa.
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Biggs said Saturday was a success.
Antifa stands for anti-fascist and refers to a loose worldwide coalition of activists and protesters who oppose far-right ideology.
City officials are actively discouraging people from participating in any of the demonstrations. For NPR News, I'm Meerah Powell in Portland, Ore. "That's all we wanted".
"We need to continue to confront ... the reality of the growing white nationalist movement and white supremacy in the United States", Wheeler continued.
The latest rally began late Saturday morning. Both groups of protesters are now divided.
Proud Boys says incidents of violence allegedly involving members of the loosely organised antifa movement, an global coalition of militant activists and protesters opposed to the far right - justifies a ban.
Meanwhile, the counter-demonstration included antifa members dressed all in black, many wearing masks.
Thirteen people were arrested as police declared a civil disturbance. The Southern Poverty Law Center, a major USA civil rights organisation, has classified it as a hate group.
Ward said even if right-wing groups return to Portland he is confident in the community's ability to turn out and stay true to its values.