Jeremy Joseph Christian, 35, is charged with murder, attempted murder, possession of a weapon and intimidation.
During his brief appearance, he shouted slogans such as: "You call it terrorism. I call it patriotism."
He could also be heard shouting "Death to the enemies of America".
"Leave this country if you hate our freedom - death to antifa," he said, using a common abbreviation for the anti-fascist movement.
He did not enter a plea to the charges and is due to appear in court again on 7 June.
President Donald Trump has tweeted that last week's attack was "unacceptable".
Portland's mayor is meanwhile trying to ban a forthcoming right-wing rally in the West Coast city.
The attack unfolded on Friday afternoon after the suspect began spewing "hate speech" towards two young women on a train, police said.
Taliesin Namkai-Meche, 23, and Ricky Best, 53, intervened and were fatally stabbed at the Hollywood Transit Center train station, said investigators.
Another man, Micah David-Cole Fletcher, was slashed in the neck and is recovering. He was in court on Tuesday to see Jeremy Joseph Christian's appearance.
Destinee Mangum, 16, said she had been with a friend wearing a hijab on the first night of Ramadan - Islam's holiest month - when the suspect targeted them.
"He told us to go back to Saudi Arabia, and he told us we shouldn't be here, to get out of his country," she told KPTV-TV.
"He was just telling us that we basically weren't anything and that we should kill ourselves."
The mother of Namkai-Meche, Asha Deliverance, took to Facebook to write an open letter to President Donald Trump, urging him to "take action".
"Your words and actions are meaningful, here in America and throughout the world," she wrote.
"Please encourage all Americans to protect and watch out for one another. Please condemn any acts of violence, which result directly from hate speech & hate groups.
"I am praying you will use your leadership to do so."
Detectives say they are investigating Mr Christian's background of extremist ideology.
At a "Free Speech" rally in Portland on 29 April, police confiscated a baseball bat he had allegedly been using to threaten liberal protesters.
Mr Christian was later filmed performing a Nazi salute, and shouting racial epithets while wearing an American flag as a cape.
On his Facebook page he has praised Oklahoma City bomber Timothy McVeigh and posted a death threat against Hillary Clinton.
And he wrote: "If Donald Trump is the Next Hitler then I am joining his SS".
Mr Christian has also voiced support for Senator Bernie Sanders, the Wall Street-bashing, 2016 Democratic presidential candidate.
According to the Oregonian newspaper, Mr Christian pleaded guilty in 2002 to robbing and kidnapping the owner of a store.
In 2010 he was charged with theft and being a felon in possession of a firearm.
Mayor Ted Wheeler said he welcomed the president's tweet on Monday condemning the attack.
But he urged the federal government to revoke a permit for a "Trump Free Speech Rally" scheduled for this weekend in Portland.
He said the organisers are "coming to peddle a message of hatred" and that hate speech is not protected by the US constitution.
A Facebook page for the event says there will be speakers and live music in "one of the most liberal areas on the West Coast", and thanks Mr Trump "for all you have done".
Mayor Wheeler also asked the federal government to deny a permit for a "March Against Shariah" planned in Portland for 10 June.
"Our City is in mourning, our community's anger is real, and the timing and subject of these events can only exacerbate an already difficult situation", said the city leader.
The American Civil Liberties Union defended the rallies, saying in a series of tweets that "the government cannot revoke or deny a permit based on the viewpoint of the demonstrators. Period".
Various fundraising websites for the victims have raised more than $1m (Â£777,000) since Friday.
A suspect accused of fatally stabbing two people on a train in Oregon, after they intervened in his alleged anti-Muslim rant, has appeared in court.