The Democratic presidential candidate Kamala Harris has called on Twitter to suspend Donald Trump’s account over his tweets suggesting the US would erupt into civil war if he were impeached.

In a letter addressed to Twitter’s CEO, Jack Dorsey, on Wednesday, Harris referenced six tweets from Trump’s account she said violated the site’s terms that users “may not engage in the targeted harassment of someone or incite other people to do so”.

The president’s tweets, which drew widespread condemnation this week, have targeted the whistleblower who exposed Trump’s dealings with Ukraine, accusing the person of being a “spy” who may have committed treason. Others quoted threats of a “civil war” that would break out if he were impeached.

Harris, a California senator, wrote: “No user, regardless of their job, wealth, or stature should be exempt from abiding by Twitter’s user agreement, not even the President of the United States.”

Trump’s rhetoric on the social network, where he has more than 65 million followers, has long been controversial – but this week it has proved especially divisive, in the wake of the House impeachment inquiry.

It’s not the first time Twitter has faced calls to censor Trump, but it has defended its position by saying these rules are more lenient for conversations that are “in the public interest”. In June, it announced a new feature under which tweets from politicians and others deemed as meeting a standard of “public interest” would remain on the platform even if they violated Twitter rules. The “public interest” feature only applies to verified accounts of elected officials with more than 100,000 followers.

But tweets from non-political accounts have also come under fire after Twitter failed to censor them in recent days. Tweets from the radical anti-government group the Oath Keepers suggesting civil war remained live on the account more than 24 hours later despite many users saying they were reporting them to Twitter’s safety team.

“This is where we are,” one tweet read. “We ARE on the verge of a HOT civil war. Like in 1859. That’s where we are. And the Right has ZERO trust or respect for anything the left is doing. We see THEM as illegitimate too.”

Oath Keepers is an extremist group that claims to have tens of thousands of former and present law enforcement officials as members, according to the anti-hate organization the Southern Poverty Law Center, which says “the entire organization is based on a set of baseless conspiracy theories about the federal government working to destroy the liberties of Americans”.

The tweets apparently did not violate Twitter’s terms of service agreement, under which communications that promote violent extremism are not allowed.

“I can’t believe I have to say this, but a heavily armed extremist group tweeting out threats of war and violence is a credible threat,” Nandini Jammi of the social media activism organization Sleeping Giants said. “The fact that they’ve decided to leave the tweet up without providing an explanation suggests that they’ve made a decision they’re unable to justify. In that case, why even bother having a terms of service?”

Other platforms are also struggling to regulate such conversations. In September, Facebook’s vice-president Nick Clegg announced the platform would be giving politicians more freedom than other users regarding hate speech – a decision that many people, including a former Facebook employee who wrote the platform’s content rules – have questioned.

Platforms have started policing some controversial accounts in the past year. In May, Facebook removed prominent accounts promoting white nationalism, including the far-right figures Milo Yiannopoulos, Alex Jones and Laura Loomer. Twitter has removed Alex Jones and Martin Shkreli for spreading hate and misinformation in the past.

“Others have had their accounts suspended for less offensive behavior,” Harris wrote. “And when this kind of abuse is being spewed from the most powerful office in the United States, the stakes are too high to do nothing.”

Twitter did not immediately offer a response to the letter from Harris.