(CNN) - Senate Majority Leader Mitch McConnell told a Kentucky radio station Thursday the Senate will put the issues of background check legislation in addition to "red flag" laws "front and center" when the body reconvenes after its summer recess, but it will not return early as Democrats are demanding.
"Those are two items that for sure will be front and center," McConnell told NewsRadio 840 WHAS.
McConnell made no commitments what would come to the Senate floor, suggesting that the negotiations are ongoing still.
But the Republican senator also said he won't call lawmakers back to Washington this month to address gun violence, following two mass shootings that left more than 30 people dead over the weekend.
"If we did that we would just have people scoring points and nothing would happen," McConnell said in the brief interview. "If we do it prematurely it will just be another frustrating experience for all of us and the public."
Still, McConnell said bipartisan discussions are happening over the August break and he said when lawmakers come back they will hopefully pass something.
McConnell specifically mentioned as possible options under consideration a background checks measure jointly sponsored by Democrat Sen. Joe Manchin of West Virginia and Republican Sen. Pat Toomey of Pennsyvanila. Trump has spoken to those two senators about the bill in recent days. McConnell also noted Sens. Lindsey Graham of South Carolina and Richard Blumenthal of Connecticut efforts on red flag laws.
McConnell said that in a conversation with President Donald Trump on Thursday morning, the two Republican leader agreed they both want a result and not just endless finger pointing.
"The key to this honestly is making a law, not making a point," he said. "The urgency of this is not lost on any of us."
McConnell, who has been recovering at home from a fractured shoulder, has faced particular scrutiny in recent days for his refusal to take up measures passed by the Democratically controlled House. His obstruction to advancing Democratic legislation has led demonstrators to protest his actions -- some coming all the way to his home in Kentucky.
For those protesters, McConnell had a message for them Thursday.
"I will not be intimidated by you people -- not a chance," McConnell said. "Not a single thing you do is going to alter how I operate on behalf of my constituents and the country."
CNN's Allison Gordon contributed to this report.
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