Majority Leader Mitch McConnell, R-Ky., vowed Tuesday to bring gun control legislation to the Senate floor so long as such a measure has received President Donald Trump's blessing.

In an interview with conservative radio host Hugh Hewitt, McConnell said the White House "is in the process of studying what they're prepared to support, if anything," in the wake of mass shootings in Texas and Ohio.

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"I expect to get an answer to that next week," McConnell said of gun control measures Trump would be willing to support. "If the president is in favor of a number of things that he has discussed openly and publicly, and I know that if we pass it, it will become law — I'll put it on the floor."

McConnell's remarks come amid renewed public pressure to tighten the nation's gun control laws. In August, two back-to-back mass shootings in El Paso, Texas, and Dayton, Ohio, left 31 people dead and more than 50 others injured. Over the weekend, a gunman in Odessa, Texas, killed seven people and left at least 25 others wounded in a shooting rampage. Those mass casualty incidents have increased pressure on Congress to pass gun control legislation when it returns next week from its summer recess.

Among the ideas under discussion are so-called red flag laws, which would allow a family member or a law enforcement official to petition a court for an order to temporarily confiscate firearms from individuals who may pose a danger to themselves or others. The orders also bar the person they cover from purchasing a firearm.

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Democrats have argued that red flag laws are not enough to prevent more bloodshed and have urged McConnell to allow a vote on the House's universal background legislation, which passed earlier this year.

So far, that bill has not received support from a single Republican in the Senate, who are unlikely to throw their weight behind any gun control measure unless its supported by Trump. The Republican Party is defending 22 states in the 2020 election cycle and nearly all are in deeply red states.

Asked on Tuesday why he won't take up the House-backed universal background check bill to the Senate floor, McConnell claimed that lawmakers and the White House were currently in a "discussion" about how to tackle "the gun issue."

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"I said several weeks ago that if the president took a position on a bill, so that we knew we would actually be making a law and not just having serial votes, I'd be happy to put it on the floor," McConnell said.

McConnell appeared to be referring to a radio interview he did in early August, where he closed the door on reconvening the Senate early from its summer recess in order to take up gun control legislation. At the time, McConnell predicted that red flag laws and expanding background checks would be "front and center" in the debate about what, if any, gun control legislation to pass.

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Another measure under consideration is a bill from Sens. Joe Manchin, D-W. Va., and Pat Toomey, R-Pa.,that would expand background checks to all gun sales, including those they place at gun shows. That measure has failed twice in the Senate, and it is unclear whether it could attract enough support from Republicans go pass.

Additionally, Sens. Lindsey Graham, R-S.C., and Richard Blumenthal, D-Conn., have said they are working on a red flag, which would offer federal grants and other incentives for states to adopt such laws. The measure would allow family members and law enforcement officials to request that a court temporarily restrict the access to firearms from individuals whom they believe could pose a threat to themselves or others. A similar bill was proposed last year by Sen. Marco Rubio, R-Fla., and former Sen. Bill Nelson, D-Fla.

Trump has floated various ideas to curb gun violence since the Dayton and El Paso shootings, but he has not yet thrown his support behind a specific measure.

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The president has, at times, appeared open to expanding background checks. In the days following the shootings in El Paso and Dayton, Trump tweeted that "serious discussions are taking place between House and Senate leadership on meaningful background checks." But he later reportedly told Wayne LaPierre, the chief executive of the National Rifle Association, that background checks were off the table.

After the shooting this past weekend, Trump called for changes to the nation's mental health system as a solution to prevent mass shootings.

"It would be wonderful to say — to say 'eliminate,' but we want to substantially reduce the violent crime — and actually, in any form. Any of its evil forms. This includes strong measures to keep weapons out of the hands of dangerous and deranged individuals, and substantial reforms to our nation's broken mental health system," Trump said on Sunday.

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He also appeared to dismiss the effectiveness of background checks in preventing or stopping mass shootings, claiming that "as strong as you make your background checks, they would not have stopped any of it."