And he indicated that naming antifa "an organisation of terror" was being considered.
Police set up concrete barriers and closed streets and bridges in an effort to contain and separate the rival groups, after seizing metal poles, bear spray, shields and other weapons.
Leaders of the right-wing groups vowed to return to Portland, saying they would keep coming back to the liberal West Coast city so long as the left-wing antifascists, known as antifa, groups remained active.
While the mayor's remark might have raised some eyebrows, Portland police chief Danielle Outlaw reported that 13 people have been arrested in connection with the turmoil, including for disorderly conduct, interfering with police, resisting arrest, possession of a weapon and unlawful use of a weapon.
"That group of antifa there in Portland needs to be exposed for who they are", Biggs told the Associated Press Tuesday. The groups gathered on both sides of the Willamette River, which runs through the city.
More than two dozen local, state and federal law enforcement agencies, including the FBI, are in Portland, Oregon, to help police with a right-wing rally Saturday that's expected to draw demonstrators from around the U.S.
In the days leading up the event, Portland Mayor Ted Wheeler said people who espoused hate or engaged in violence were "not welcome".
Mr. Trump took aim at antifa from his Twitter account ahead of the "End Domestic Terrorism" rally getting underway in Portland, Oregon, where authorities have braced for possible clashes erupting between demonstrators and counterprotesters.
It isn't clear what Trump meant in his tweet as there's no mechanism for the government to declare a domestic organisation a terror group.
The Portland Police Bureau held a media briefing Friday, outlining its plans for the scheduled demonstration that is attracting far-right figures from across the country and prompting local counter-protests.
"And frankly, it's not helpful", Wheeler added.
Joe Biggs, the organiser of the right-wing gathering, said it was a success. He was at a confrontation that broke out on May 1 outside a bar where members of the so-called "antifa" movement had gathered after a May Day demonstration.
Police Lt. Tina Jones said Saturday afternoon that hundreds of demonstrators have gathered in and around downtown for hours.
A video of that attack went viral and led the Proud Boys, who have been designated a hate group by the Southern Poverty Law Center, to organise Saturday's event.
At a June rally in Portland, masked antifa members beat up a conservative blogger named Andy Ngo. Joining them were the American Guard, Three Percenters, Oathkeepers and Daily Stormers.
Gibson's attorney, Multnomah county Republican chair James Buchal, said in a statement the charges were "part and parcel of the dishonest campaign by Portland leaders to blame out-of-town demonstrators for violence that began and persists because antifa wants to shut down any rightwing demonstrations in Portland".