Both Bush and Walker, like most Republicans, staunchly oppose the Iran deal. But Walker, the governor of Wisconsin, is seeking to portray himself as a tougher critic. In the video, he is shown telling a crowd that he would "terminate" the deal on day one of his presidency if Congress does not derail it first.
The video comes as Walker has struggled in the polls in recent weeks amid the rise of Donald Trump. Walker's broadside against Bush is a notable departure from his strategy of generally avoiding direct criticism of his opponents.
Mike Murphy, a longtime Bush strategist who is leading a super PAC supporting his campaign, criticized Walker's video.
"Jeb strongly opposes Iran deal. Walker distracted; focused on his plan to build wall with... Canada. #NotReady" Murphy tweeted in response to a reporter tweeting a shorter version of Walker's video.
Murphy's reference is to Walker
on NBC's "Meet the Press" that discussion of a wall along the U.S.-Canada border is "a legitimate issue for us to look at."
Murphy's tweet set off a back-and-forth on Twitter with Walker campaign manager Rick Wiley, with Wiley taking shots at Bush on Iran and Murphy going after Walker on immigration and abortion and staffing questions.
Walker is planning a campaign swing through Texas later this week that will take him on Friday to Midland, where Bush was born.
Bush also took a fresh round of criticism from Trump on Monday. The real estate mogul who has surged to the top of the polls put out a video attacking Bush for once suggesting that undocumented immigrants entered the United States as "an act of love."
"Mr. Trump's immigration plan is not conservative, would violate the Constitution and cost hundreds of billions of dollars, which he will likely attempt to pay for through massive tax hikes," responded Bush spokeswoman Kristy Campbell.
Philip Rucker and Jenna Johnson contributed