Police identified the assailant, who was arrested soon after the Friday afternoon attack, as Jeremy Joseph Christian of Portland, a 35-year-old convicted felon.
A senior researcher with the Southern Poverty Law Center, in a blog post, said Christian's Facebook page showed he held "some racist and other extremist beliefs."
The attack unfolded hours before the start of Ramadan, Islam's holy month, when most of the world's 1.6 billion Muslims observe a daily religious fast.
Christian started shouting ethnic and religious slurs, apparently at the two young women, one of whom wore a Muslim head-covering, the Portland Police Department said in a statement.
Three men who intervened were stabbed. One died at the scene, another died at a hospital, and the third was treated for non-life-threatening injuries, police said.
Christian was booked on two counts of aggravated murder and charges of attempted murder, intimidation and being a felon in possession of a restricted weapon, and was ordered held without bail.
The women left the train before officers arrived, police said.
Dyjuana Hudson, the mother of one of them, told The Oregonian newspaper her 16-year-old daughter, who is black, boarded the train with a Muslim friend, also a teenager, who was wearing a hijab.
The attacker approached the girls while screaming at them, Hudson told the newspaper, relaying an account her daughter had given her. "He was saying that Muslims should die," Hudson said.
On Friday police said detectives wanted to speak to the two women. A detective later took a statement from her family, Hudson told the paper. She could not be reached for comment.
Police declined to release details of Christian's criminal history. But the newspaper reported he had been convicted of robbery, kidnapping and weapon charges, citing court records. It was not immediately clear if he had obtained an attorney.
In a statement, the Council on American-Islamic Relations blamed an increase in anti-Muslim incidents in part on President Donald Trump's focus on militant Islamist groups and anti-immigrant rhetoric.
The administration has said that while it strongly opposes Islamist militants, it has no quarrel with Islam.
A Facebook page that appears to belong to Christian mentions "Jihadi Muslims" among people he disliked. The image on the page matches a photo of Christian released by police.
"If Donald Trump is the Next Hitler then I am joining his SS to put an end to Monotheist Question," a rambling post on Jan. 23 reads.
The page includes images of Christian raising his right hand in a Nazi-like salute at a "Free Speech" protest in Portland last month.
Thumbnail Credit: REUTERS, Bureau/Handout