Former Florida Gov. Jeb Bush (R) used a quick-witted Twitter response Thursday against Donald Trump, in the latest escalation of the feud between the two Republican heavyweights.

Following a press conference on Tuesday during which Trump announced that he would sign a pledge not to run as a third-party candidate if he loses the Republican nomination, Bush's Twitter account immediately posted a photo bragging about his lengthy history as a Republican.

The spat between the two candidates has escalated, as Bush has shifted strategy to more directly go after Trump amid his rise in polls.

Bush's communications director Tim Miller told Business Insider last month that the campaign would begin shining a light on Trump's past connection to Democratic lawmakers.

"As it's become clear that Mr. Trump is trying to run a legitimate campaign rather than a reality-TV stunt, the result is that he has to deal with the scrutiny into one’s record that comes with being a candidate," Miller said.

Bush has hit Trump for being a "fake conservative," while Trump has repeatedly labeled Bush as "low energy."

"I watched him on TV this morning, and it was a bit sad," Trump said Thursday when asked about Bush's attacks. "He was supposed to win, and he just doesn't have the energy."

Bush's tweet is also part of a larger push by the campaign to engage opponents on social media in order to spotlight the former governor's conservative record.

While the candidates rarely personally engage with each other on the campaign trail, Twitter exchanges gin up attention, and generally garner far higher levels of engagement than normal tweets.

A Twitter spokesperson told Business Insider last month that a back-and-forth between Bush and Democratic front-runner Hillary Clinton's received 5.8 million impressions, or the number of times that a tweet has been seen by users.

Miller noted that spat between Bush and Clinton was successful not only in reaching more people, but in attracting the attention of users who may not be as politically engaged.

"Reaction has been very positive. You get feedback from people who don't usually follow the day-to-day political news so you can reach a broader audience," Miller said in an email last month.