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Senate Majority Leader Mitch McConnell, R-Ky., told "The Daily Briefing" Wednesday that President Trump should "reconsider" his threat to veto a bill to fund the military for the 2021 fiscal year if it includes a provision to rename military bases named after Confederate military leaders.

"I would hope the president really wouldn't veto the bill over this issue," McConnell told host Dana Perino. "In the bill, there’s a requirement of a three-year study about changing the names. To me, this is quite different from trying to airbrush the Capitol of every statue."

TRUMP SAYS HIS ADMINISTRATION 'WILL NOT EVEN CONSIDER' RENAMING MILITARY BASES NAMED FOR CONFEDERATES

Late Tuesday, Trump tweeted that he would veto the National Defense Authorization Act (NDAA) if it included an amendment from Sen. Elizabeth Warren, D-Mass., to rename at least 10 military installations, including Fort Hood in Texas, Fort Benning in Georgia and Fort Bragg in North Carolina.

"I will Veto the Defense Authorization Bill if the Elizabeth 'Pocahontas' Warren (of all people!) Amendment, which will lead to the renaming (plus other bad things!) of Fort Bragg, Fort Robert E. Lee, and many other Military Bases from which we won Two World Wars, is in the Bill!" Trump tweeted.

"I hope," McConnell repeated, "the president would reconsider vetoing the entire defense bill, which includes pay raises for our troops, over a provision in there that could lead to changing the names of some of these military bases."

SCHUMER: TRUMP WON'T VETO DEFENSE BILL DESPITE HIS THREAT TO DO SO

The majority leader also addressed the possibility of additional coronavirus relief legislation, telling Perino that if another stimulus package happens, it will happen this month.

We passed in the Senate the CARES Act and then a follow on to the CARES Act back in March.," McConnell said. "I said at the time [that] we need to take a snapshot of where the country is in July, see what kind of progress is being made by reopening the country, get an assessment of what did or didn't work and the CARES Act, and then make a decision about whether to do phase four.

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"We may well do that. And if we do it, we'll do it in July," he continued. "And I can tell you for sure that if we do another bill, it will have liability protections in it for doctors, for hospitals, for nurses, for businesses, for universities, for colleges.

"Nobody knew how to deal with the coronavirus and unless you are grossly negligent or intentionally engaged in harming somebody," McConnell added, "you’re going to be immunized from the epidemic of lawsuits that have already developed surrounding the pandemic."

Fox News' Tyler Olson contributed to this report.