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Republican presidential candidates Donald Trump and former Florida Gov. Jeb Bush argue during a Sept. 16, 2015, debate at the Reagan Library in Simi Valley, California. Getty Images

The ongoing Twitter war between the presidential campaigns of Republican front-runner Donald Trump and former Florida Gov. Jeb Bush picked up again Monday night. After the real estate mogul retweeted a series of insults directed at his rival, a Bush spokeswoman posted a message calling Trump "Twitter-drunk," Politico reported Tuesday.

The famously outspoken Trump appeared to have started the social media battle Monday at about 10 p.m. local time, when he retweeted a message from a follower calling Bush's strategy of attacking Trump "really dumb." Earlier in the day, Bush — who is in fifth place among GOP primary candidates — told reporters in Florida he wanted to debate Trump one-on-one, and at a speech last week he called the tycoon "a jerk."

After his initial post, Trump then retweeted a photo of Bush picking his nose. Business Insider reported that the picture "appear[ed] to be an altered Reuters image of Bush with a finger on his lip."

In response, Bush's national press secretary, Kristy Campbell, also got creative.

Trump continued retweeting Bush insults for about an hour, including a post saying Bush's mother planned to vote for Trump and another asking the former governor to "do us a favor and drop out."

Bush himself did not get involved in the Monday-night Twitter feud, but CNN reported he has been stepping up his criticism of Trump in recent weeks. Bush said Dec. 19 that "a guy like that should not be the front-running candidate of our great party" and that "you cannot insult your way to the presidency." Trump fired back on Twitter over Christmas, taking aim at Bush's poll numbers and campaign spending.

As of Monday morning, Trump was leading the GOP field with the support of 37.5 percent of likely primary voters, according to the survey aggregator HuffPost Pollster. Bush was in fifth place with 5.4 percent.