Portland police say suspect confronted and then shot a demonstrator who was taken to hospital with non-lethal injuries.

A police manhunt is on for a suspect who shot an anti-Donald Trump protester in Portland, Oregon, after they got into a confrontation, as demonstrations against the US president-elect continue.

Protests have taken place in various parts of the United States since Wednesday after the controversial Republican candidate Trump was elected the 45th US president.

On Saturday, hundreds resumed marches in New York City. In Chicago, hundreds more – including families with small children – chanted “No hate. No fear. Immigrants are welcome here” as they marched through Millennium Park, a popular downtown tourist attraction.

“We’re horrified the country has elected an incredibly unqualified, misogynist, racist on a platform that was just totally hateful,” said Mary Florin-McBride, 62, a retired banker from New York who held a sign reading, “No Fascism in America.”

Police said in a statement that the Portland attacker got out of his vehicle on a bridge where he confronted and then shot the anti-Trump protester, who was taken to a hospital with non-life threatening injuries.

A search was on for the gunman, who reportedly fled in the vehicle after the attack and is still at large.

Anti-Trump protests swept across the cities of Miami, Atlanta, Philadelphia, New York, San Francisco and Portland on Friday, drawing about thousands of people who voiced anger at the billionaire businessman’s controversial campaign rhetoric about immigrants, Muslims and women.

Other small demonstrations were held in US cities. Some waved American flags or carried signs reading “Not My President”.

Earlier in the night, protesters blocked traffic and threw objects at Portland police dressed in riot gear, who responded with pepper spray and flash-bang devices. At one point, police pushed protesters back and appeared to take at least one person into custody, according to footage on a local NBC affiliate.

IN PICTURES: Violence erupts as anti-Trump rallies sweeps US cities

Hundreds joined a “Love Rally” on Friday afternoon in Washington Square Park in New York City’s Manhattan.

In Los Angeles on Thursday night, police arrested about 185 people, mostly for blocking roadways or being juveniles out past curfew, according to police.

One officer was treated in hospital for injuries suffered during the protest.

Anti-Trump demonstrators have voiced concerns that his presidency, due to start on January 20, would infringe on Americans’ civil and human rights.

They cited his campaign promises to restrict immigration and register Muslims, as well as allegations against the former reality-TV star that he had sexually abused women.

Protesters in various cities have chanted slogans and carried signs reading “Impeach Trump”.