He said he spoke to the state's Democratic governor, Tim Walz, and "told him that the Military is with him all the way".
Mr Trump added: "Any difficulty and we will assume control but, when the looting starts, the shooting starts".
The singer criticised Mr Trump for his response to violent protests in Minneapolis over an incident where a black man died while being arrested.
That came after Trump signed an executive order on Thursday threatening new regulations on social media firms.
"He is calling for violence against American citizens during a moment of pain for so many".
Donald Trump then lasts his tough talk towards the protestors in yet another tweet that read, "These THUGS are dishonoring the memory of George Floyd, and I won't let that happen". However, Twitter has determined that it may be in the public's interest for the Tweet to remain accessible. A user looking at Trump's timeline would have to click to see the original tweet.
CNN has not been able to locate the person that took the video.More news: Mercedes responds to 'unfounded and irresponsible' F1 exit reports
President Trump attempted to clarify his Friday morning tweet that said "when the looting starts, the shooting starts", writing on Friday afternoon that the controversial tweet was "spoken as a fact".
"The media, Joe Biden, and the Democrats pounced, purposefully misrepresenting what the President had said, and showing once again that they are incapable of resisting their base impulse of dividing Americans, exclusively for the goal of political gain, ratings, and cable news profit", said Trump campaign manager Brad Parscale.
Protests took place in other US cities, including Louisville, Kentucky, where police said seven people were shot.
"We could have our military there very quickly", if their help was requested, Trump said on Saturday afternoon. "I think the difference is a November election". "Honor the memory of George Floyd!" the president added. Trump has condemned the killing and promised justice.More news: Grimes is selling her soul to the highest bidder, for art
Yet Trump has a long history of injecting himself into racially sensitive cases.
Trump's repeated condemnation of the killing and outreach to the man's family was a marked change in tone from his earlier comments that also invoked a civil-rights-era phrase fraught with racist overtones.
And he has even appeared to advocate for the rougher treatment of people in police custody, speaking dismissively of the police practice of shielding the heads of handcuffed suspects as they are being placed in patrol cars.More news: BMW 6 Series GT packs new look, tech, mild hybrid power