Sen. Chuck Grassley said Thursday that he plans to sit down with Sens. Dianne Feinstein and John Cornyn to discuss "what sort of agreement we can reach on legislation" in response to gun violence. During a Senate Judiciary Committee meeting to consider nominations and sentencing reform, Grassley, the panel's chairman, spoke about the shooting at Marjory Stoneman Douglas High School a day earlier that left 17 people dead and more than a dozen people wounded.

"The three of us are going to sit down and talk about this," said Grassley, an Iowa Republican, about meeting with Cornyn, the Senate majority whip, and Feinstein, the top Democrat on the committee.

Grassley said that he had discussed a meeting among the three of them with Cornyn earlier this week, before the tragedy that unfolded on Wednesday in Parkland, Florida. He said that in addition to the "common denominator of guns," mental illness is also an issue that must be addressed.

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"Today, grief and sorrow on our part is really not adequate because, for the past 25 years, I have seen this committee do exactly that and do nothing," Feinstein said. "This isn't going to stop, members. This is going to continue. And we become culpable when we do nothing to stop it."

Chairman of the Senate Judiciary Committee Charles Grassley, R-Iowa, speaks during the second day of confirmation hearings on the nomination of Sen. Jeff Sessions, R-Ala., to be U.S. attorney general in Washington on Jan. 11, 2017. REUTERS/Joshua Roberts

Feinstein noted that after the Las Vegas massacre last October that left 58 people dead, she had introduced legislation to ban bump stock devices, which convert semiautomatic weapons to automatic ones, that was never considered.

"We can't get any action on this proposal," she said, adding that it's "so frighteningly easy" to obtain guns in the U.S.

Following the mass shooting in Sutherland Springs, Texas last November, Cornyn introduced bipartisan legislation that would enhance compliance and accuracy of existing background check systems in place for firearm purchases. The measure has not yet been considered.