They were mainly young people saying a Trump presidency would create deep divisions along racial and gender lines.
However, police in Portland said they were dealing with vandalism and aggressive behaviour.
In response, President-elect Donald Trump tweeted that the protests were “very unfair”.
Earlier, Donald Trump met President Barack Obama at the White House and described him as a good man.
However, despite their cordiality, Donald Trump is intent on dismantling much of President Obama’s legacy. That includes ObamaCare, the act extending medical insurance to more Americans than ever before.
Crowds of protesters gathered in cities across the country on November 10.
Police in Portland, Oregon said the protest there should be considered a riot, with shop windows being broken, some demonstrators carrying bats and others arming themselves with rocks.
There were no reports of violence at the other protests, although demonstrators in Minneapolis briefly blocked an interstate highway in both directions.
In Philadelphia, crowds gathered near City Hall holding placards bearing slogans such as “Not Our President”, “Trans Against Trump” and “Make America Safe For All”.
In Baltimore, police said a peaceful crowd of 600 people marched through the city, blocking traffic. In San Francisco, high school students waved rainbow banners and Mexican flags.
A small crowd also gathered outside Trump Tower in Chicago, a day after thousands marched through the city centre. Some passers-by cheered them but at least one driver shouted that they should “shut up and accept democracy”, the AP reported.
Protesters also returned to Trump Tower in New York for a second night.
In his tweet, Donald Trump described them as “professional protesters” and said they had been “incited by the media”.
Meanwhile Mexico’s President Enrique Pena Nieto said he was optimistic his country could have a positive relationship with the US under President Donald Trump, despite his anti-Mexican rhetoric during the campaign.
Enrique Pena Nieto said he and Donald Trump had agreed to meet, possibly during the transition period before President Trump’s inauguration in January.
In Russia, President Vladimir Putin’s spokesman said Donald Trump and the Russian president were “very much alike” in how they see the world.
Dmitry Peskov said Russian experts had been in contact with some members of Donald Trump’s staff during the campaign.
However, he said the Russian government had nothing to do with the theft of emails from the Democratic campaign that were later published by WikiLeaks.
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