Mexico has said it would not pay for a border wall.
Corker has a mixed relationship with the president, despite being rumored as a possible Vice Presidential candidate in 2016 and golfing with the president and Tennessee football legend Peyton Manning.
It was a new moniker for the House minority leader, and Trump doubled down on controversial comments he'd made earlier this month about the drug gang. The two continued to trade insults a year ago, with Trump giving the senator the nickname "Liddle Bob Corker" and insisting he wouldn't even be able to get elected "dog catcher" if he tried running for re-election.
"We're going to defend our borders, and we're going to fight crime", he said.
"They're not human beings".
Trump travelled to Nashville, Tennessee, as he steps up his efforts to stop Democrats aiming to regain control of the House or Senate - if not both.
Subtropical Storm Alberto forms in western Caribbean
The system is expected to intensify during the weekend and will likely consolidate into a tropical storm at some point on Sunday. He said: "Coastal flooding can occur along Florida's west coast and the coastal communities of the panhandle".
"We did it and we did the right thing", said Trump. Tennessee is considered a solidly Republican state, but it could provide an opportunity for Democrats to pick up a seat come November. When Trump introduced Corker at the rally, he was met with audible boos from the audience.
Blackburn, a Republican congresswoman, is vying for her party's nomination to replace retiring Corker, a Republican.
For Trump, the trip to Tennessee comes as part of a ramped-up midterm travel schedule.
Mexican President Enrique Pena Nieto quickly replied to Trump Tuesday, writing on his Twitter account - in English, which Pena Nieto seldom does - "NO. Mexico will NEVER pay for a wall".
"In the end, Mexico is going to pay for the wall, I'm just telling you that", he said, pointing to negotiations to change the North American Free Trade Agreement. "They don't want the wall, they want open borders, they're more interested in taking care of criminals than they are of taking care of you - Bredesen donated a lot of money to the campaigns of Barack Obama and Hillary Clinton". "They do nothing for us".
Tuesday night in Nashville was one to remember. Not now, not ever. "Sincerely, Mexico (all of us)".