In a Medium post and a series of tweets on Friday afternoon, the former congressman from El Paso said: "Our campaign has always been about seeing clearly, speaking honestly, and acting decisively".
"My service to the nation are seemingly to be no longer as a candidate or because the nominee", he wrote on Twitter.
O'Rourke was a member of the U.S. House of Representatives from Texas' 16th district from January 2013 to January 2019.
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Twitter had previously implemented rules and restrictions for political advertising. "It's worth stepping back in order to address", he concluded.
In a post on the Medium website, O'Rourke said he chose to run for president so he could unite "a divided country" to confront the "greatest set of challenges" faced by the U.S.
Beto O'Rourke is suspending his 2020 presidential campaign.
Carlson then compared O'Rourke supporters to those of "an indie rock band that wasn't very good but was considered cool".
When Democratic National Committee Chairman Tom Perez took the stage, he thanked Mr. O'Rourke for running and called on the crowd to give him a "special round of applause" for running a "spirited campaign". "I will do everything that I can to support the eventual nominee of this party with everything that I've got, and I encourage every single one of you to do the same", he said. He had not yet met the thresholds for participating in the upcoming primary debates in November and December. Mr. Schumer, an architect of gun control legislation in the 1990s, said he saw no support in the party for Mr. O'Rourke's stance on requiring gun owners to surrender certain firearms.
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Mr Trump was in Tupelo to campaign on behalf of the state's Republican candidate for governor, Tate Reeves, who is in a tight race against Democrat Jim Hood.
As O'Rourke leaves the campaign trail to come home to Texas, he returns to a state with a booming economy and strong job growth.
The New York Times reported that O'Rourke was not expected to run for Senate in Texas, where Republican incumbent Senator John Cornyn is up for reelection race.
His position led to criticism from Democrats in Washington, including Senate Minority Leader Chuck Schumer of NY.
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O'Rourke was one of many candidates seeking the Democratic nomination.