Texas Gov. Greg Abbott dodged major Republican challenges from far-right opponents on Tuesday, according to an Associated Press call, and staged a closely watched general election showdown against Democratic nominee Beto O'Rourke.

Abbott easily beat the field of his fellow Republicans, surpassing the 50% mark needed to avoid a runoff. His opponents included former Texas Republican Party leader Allen West and businessman Don Huffines, both of whom had sought to position themselves as a more conservative alternative to Abbott.

Abbott, who is seeking his third term, had received approval from former President Donald Trump.

"Tonight, Republicans sent the message that they want Texas to continue to be the land of opportunity and prosperity for all -- the prosperity that we have brought about for the past eight years," Abbott said during a Corpus Christi gathering.

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He now faces O'Rourke in the November 8 election.

O'Rourke, a former Texas congressman and 2020 Democratic presidential nominee, also easily won his party's nomination, according to the AP.

"THANK YOU TEXAS," O'Rourke wrote in a Twitter message to his followers. "We will win this race together for each other."

Primary polls showed Abbott topping O'Rourke, and Texas hasn't elected a Democratic governor in more than three decades.

But O'Rourke emerged as the new face of the Texas Democratic Party in 2018 as he inspired a new generation of voters while running against Republican Sen. Ted Cruz.

Though he was beaten in that contest, O'Rourke stayed in the public spotlight and rode a wave of Betom-mania in the 2020 Democratic presidential primary, where he took left-wing positions that could complicate his efforts to appeal to Texans.

And the landscape in 2022 will likely be a far cry from that of 2018 and 2020. Biden's ratings are low - an ominous warning for downgraded Democrats.

O'Rourke has criticized Abbott's conservative handling of the coronavirus pandemic and last year's power outages in Texas.