Sen. Kamala Harris (D-CA) unsuccessfully tried at Tuesday's Democratic presidential debate to win Sen. Elizabeth Warren (D-MA) over to her push for Twitter to ban Donald Trump, an issue that is quickly becoming a signature of Harris' presidential bid.

Harris told Warren that she was "surprised" the Massachusetts senator hadn't backed her call, issued in early October, for Twitter to ban Trump from its site. In her letter to Twitter, Harris cited Trump's attacks on the Ukraine phone call whistleblower and his tweet about "civil war" as reasons for Twitter to deplatform the president.

"I would urge you to join me because here we have Donald Trump, who has 65 million Twitter followers and is using that platform as the president of the United States to openly intimidate witnesses, to threaten witnesses, to obstruct justice," Harris told Warren during the debate. "And he and his account should be taken down."

Warren demurred, saying that she was focused on beating Trump in the presidential election.

"Look, I don't just want to push Donald Trump off Twitter," Warren said. "I want to push him out of the White House. That's our job."

Harris continued to press Warren to call for Trump to be banned from Twitter.

"So join me in saying that his Twitter account should be shut down," Harris said.

"No," Warren said.

"No?" Harris said.

Twitter announced new rules Tuesday for tweets from Trump and other world leaders that may violate the site's rules. The new rules include a provision making it harder to share tweets that violate Twitter policies.

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