Trump said Thursday that he would give her a DNA test in the middle of a debate and say: "I'll give you a million dollars for your favorite charity, paid for by Trump, if you take the test and it shows you're an Indian".
Trump also used his Montana speech to deride Rep. Maxine Waters, the veteran Democratic lawmaker from California whose call for aggressive protests against Trump administration officials drew the president's ire last month. He has been sued for defamation by an adult film actress, Stormy Daniels, for calling her a liar for claiming she had an affair with Trump in 2006.
Tester, the top Democrat on the Senate Veterans' Affairs Committee, led the charge against Jackson, the White House physician who was briefly Trump's pick to lead the embattled agency.
Rallies like the one on Thursday also showcase a November strategy that combines sweet spot issues like immigration, tax cuts, the booming economy, and attacks on kneeling National Football League players with nostalgic reminiscences of his 2016 campaign that Trump loves.
"If you want to protect your families and your community, then you have no choice", Trump said. Trump also claims that Democrats "couldn't give a damn" about law enforcement.
Trump also talked tough about upcoming meetings in Europe with members of the North Atlantic Treaty Organisation military alliance and Russian President Vladimir Putin.
Trump was scheduled to hold a rally in the city of Great Falls to campaign for Tester's Republican challenger, State Auditor Matt Rosendale.
"If you tune in Monday at 9 o'clock, I think you're going to be extremely happy", he said, teasing his crowd on Thursday about his nominating announcement next week.
Trump also scoffed at journalists for questioning his readiness to meet with Putin, a former spy, in Finland on July 16.
His barbs against the media came on a day when newsrooms across the US held a moment of silence in remembrance of five Maryland newspaper staffers who were fatally shot last week by a man who authorities say held a grudge against the publication.
Thousands of people stood in line for hours to get into the Four Seasons Arena ahead of President Donald Trump's rally in Great Falls.
The support for Cruz belies Rosendale's attempt to tie himself to Trump, but seemingly did not - because of Trump's visit - run afoul of a loyalty test the White House is running when deciding endorsements in the midterms. Jackson, a Navy rear admiral, denied the claims but withdrew his nomination.
Trump's rally on Thursday was a classic display of virtuoso demagoguery and hardball populism that has already been aimed at red-state Democrats like Sens.
"Because we're in the MeToo generation", he said at a political rally in Montana, referring to the movement against sexual misconduct by powerful men.
USA intelligence agencies say Putin meddled in the 2016 election to benefit Trump. Rosendale said he'll back Trump's agenda, while Tester said he'll support the president when it's in the state's interests and oppose him when it's not.
The first and most important question - one Trump frequently raises during his travels - is whether he can defy historic omens and re-create robust turnout from his most loyal supporters that would mirror his stunning 2016 race and help lift Republican candidates.
Chris Meagher, Tester's spokesman, said the campaign was "glad to hear President Trump is finally coming to Montana, after Jon has invited the Administration several times to Montana to discuss topics important to Montanans".
"Welcome to Montana, and thank you President Trump for supporting Jon's legislation to help veterans and first responders, hold the VA accountable, and get rid of waste, fraud and abuse in the federal government", the ad read.
The play by Tester's campaign underscored the hard re-election campaign facing Tester in this deeply red state where Trump beat Hillary Clinton by 20 points in 2016.