2020 Democratic U.S. presidential candidate and U.S. Senator Kamala Harris (D-CA) speaks at the Iowa State Fair in Des Moines, Iowa, August 10, 2019.

Democratic presidential hopeful Kamala Harris called on Twitter's CEO on Tuesday to consider suspending President Donald Trump's account, saying his tweets violate the site's anti-bullying policy.

In a letter to Twitter's Jack Dorsey, the senator from California pointed to a series of tweets from the president referring to the whistleblower who filed a complaint about Trump's July 25 call with the president of Ukraine. Harris said Trump's tweets were an attempt to "target, harass" and "out" the whistleblower.

Harris also pointed to Trump's tweet that "a Civil War" could break out if Democrats successfully remove the president from office. She said the tweet suggests "that violence could be incited should Congress issue formal articles of impeachment against him."

"Time to do something about this," Harris tweeted to Dorsey. She included Trump's tweet calling the impeachment inquiry a "COUP."

Harris tweet.

Twitter said it plans to respond to the letter.

A White House spokesperson told CNBC in an emailed statement, "It is not surprising that Kamala Harris, someone who believes in bigger government and more regulation, would like to silence her political opponents. In fact, it's rather authoritarian of her. President Trump's use of technology to communicate directly with the American people and share his Administration's unprecedented accomplishments should be praised, not criticized."

Harris' letter touches on a longstanding issue for Twitter in how it deals with accounts from world leaders who violate its policies. In June, Twitter announced that it would flag, but not remove, abusive tweets from world leaders. In what amounted to a compromise, Twitter said it would put a disclaimer on such tweets and make it harder for them to spread. Still, Twitter said it would keep the messages on the platform in case they would be in the public interest to access.

In a New York Times op-ed, technology contributor Kara Swisher wrote that Trump has been able to get away with tweets like the "Civil War" one because "the tweet's message was implicit rather than explicit."

"The company's weak response shows how utterly incapable it is in dealing with these thorny issues," Swisher wrote.

On Wednesday, fellow Democratic presidential candidate Elizabeth Warren, a senator from Massachusetts, took a different stand from Harris. Asked by a reporter if Trump should be banned from Twitter, Warren simply said "no."

ABC News Tweet.

The company has taken an especially cautious approach to monitoring speech as conservative lawmakers have repeatedly accused Twitter and other tech companies of political bias.

Twitter is immune from liability from Trump and others' tweets due to a law known as Section 230 of the Communications Decency Act. Under the highly contested law, internet platforms are not legally responsible for the speech of their users. Several lawmakers have argued that the law, which originally aided the growth and innovation of nascent tech companies, is no longer appropriate for today's tech giants.

But Twitter has taken steps to remove accounts of prominent nonworld leaders who have violated its rules. Twitter announced last year, for example, that it would permanently ban right-wing conspiracy theorist Alex Jones and his company, InfoWars, from the platform after claiming the accounts had violated its abusive behavior policy. Harris referenced this ban and the suspension of "[d]isgraced hedge fund manager" Martin Shkreli and actor James Woods for past violations on the platform.

"I believe the President's recent tweets rise to the level that Twitter should consider suspending his account," Harris wrote. "Others have had their accounts suspended for less offensive behavior. 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."

Download Kamala Harris' letter to Twitter CEO Jack Dorsey or read the full letter below: