WASHINGTON (AP) — Congressional Republicans are waiting for the White House to chart a path forward on gun violence legislation, Senate Majority Leader Mitch McConnell said Tuesday, effectively putting the burden on President Donald Trump to decide the GOP's legislative response to the spate of mass shootings that included another deadly attack in Texas over the weekend.

Asked about prospects for a Senate vote on legislation passed by the Democratic-controlled House to expand background checks for gun purchases, McConnell said, "The administration is in the process of studying what they're prepared to support, if anything."

The Kentucky Republican said he expects an answer from the White House next week, adding that he wants to make sure that senators "would actually be making a law and not just having serial votes" on proposals to stem gun violence.

McConnell's comments point to the challenge ahead as Congress returns to a gun debate that emerged during their summer recess, when mass shootings in El Paso, Texas, and Dayton, Ohio, left 31 people dead. While Trump has said he wants to work with Congress to "stop the menace of mass attacks," he's waffled on support for expanding background checks, making the next steps uncertain. Trump and other Republicans have talked of pursuing other measures to address mental health or codify "red flag" laws that allow guns to be taken from people who pose harm to themselves or others, but even those measures face skepticism among GOP lawmakers.

The dynamic appears unchanged even after a shooting in West Texas over the weekend that killed at least seven people, with McConnell setting a high bar for action in the Senate when it returns next week after a five-week recess. If Trump favors background-checks or other legislation he has discussed publicly in recent weeks, and senators "know that if we pass it it'll become law," then he'll put it on the Senate floor for a vote, McConnell told radio host Hugh Hewitt.

Trump in a tweet Tuesday urged Congress to "get back to work," but omitted any reference to guns, focusing instead on prescription drug prices, health care and infrastructure.

Trump said Sunday that any gun measure must satisfy the competing goals of protecting public safety and the constitutional right to gun ownership.

"For the most part, sadly, if you look at the last four or five (shootings) going back even five or six or seven years ... as strong as you make your background checks, they would not have stopped any of it," Trump said. "So it's a big problem. It's a mental problem. It's a big problem."

Trump mentioned the need for "strong measures to keep weapons out of the hands of dangerous and deranged individuals" along with changes to a mental health system he described as "broken."

Sen. Chris Murphy, a leading gun control supporter, said Trump has told him personally that he remains committed to working on expanded background checks legislation.

Even so, the Connecticut Democrat rates the chance of Congress actually approving anything at "less than 50-50," especially if Trump appears willing "to give the NRA veto power" over legislation supported by Murphy and other Democrats, along with a handful of Republicans such as Pennsylvania Sen. Pat Toomey. Toomey and Sen. Joe Manchin, D-W.Va., are seeking to revive a bill they have long pushed to expand background checks for gun purchases.

"I am skeptical that these efforts are going to bear fruit. I think it's very hard to negotiate with this White House when the president's public positions seem to change by the day," Murphy said last month. "I'm going to try ... because the stakes are so high."

A package of bills Murphy supports would strengthen background checks and incentivize states to pass so-called "red flag" laws that allow guns to be taken from people who pose harm to themselves or others.

As senators debate their next steps, House Democrats are moving ahead on other bills, with the House Judiciary Committee set to consider a host of proposals to address gun violence at a hearing next week. The panel postponed a hearing originally scheduled Wednesday because of Hurricane Dorian. Several lawmakers on the panel represent congressional districts in Florida and Georgia, where millions of people face mandatory evacuation orders.

The committee will consider proposals to ban high-capacity magazines, establish a federal program for "red flag" laws and expand bans on firearm ownership to people convicted of certain hate crimes. The panel will also hold a hearing later this month on a bill to ban military-style assault weapons.