(CNN) —  

The father of a high school victim of last year’s deadly mass shooting in Parkland, Florida, described his Tuesday meeting to discuss gun violence with progressive activist and actress Alyssa Milano and Republican Sen. Ted Cruz as “a really important day.”

Fred Guttenberg, whose 14-year-old daughter Jaime was one of 17 people killed in the shooting at Marjory Stoneman Douglas High School, was invited to the meeting in Cruz’s Washington office by Milano after she got involved in a Twitter spat with the Texas Republican.

“I’m just truly appreciative of the chance to sit down with somebody and to have them sit down with me where we really do talk from two different sides of the room, and actually look each other in the eye,” Guttenberg told CNN’s Brooke Baldwin on “Newsroom.”

“That’s – I hope – progress. We don’t agree on prescriptions yet, you know, on what to do. But – but, you know, we agree we’re going to keep talking about it and I think that’s important,” he said.

Guttenberg called the 90-minute meeting an “important” step in discussing gun violence even as Cruz, a longtime opponent of stricter gun laws, didn’t appear to signal support for a background check bill that Guttenberg called “the most pressing thing.”

Tuesday’s meeting comes amidst a renewed debate on gun control following a string of mass shootings in the US. President Donald Trump has signaled both support and deference to addressing gun violence in recent weeks as Republican lawmakers languish over where their party stands.

Cruz tweeted after the meeting that he was “grateful for the opportunity to engage in positive, civil discussion on substantive issues.”

Speaking with CNN’s Chris Cuomo on “Cuomo Prime Time” Tuesday night, Milano said she thinks Cruz “understands” the issue but cautioned “to understand it and then to have the courage and the fortitude to do something about are two very, very different things.”

“So I’m cautiously optimistic that he knows the issue and hopeful, I guess, that he’s willing to do something about it,” she said.

The White House has remained quiet on Trump’s current stance on gun control since Congress has been back in Washington, despite calls from Senate Majority Leader Mitch McConnell for the President to make his priorities clear. Over the month-long recess, the President’s enthusiasm for legislative action has waned alongside optimism from aides that something could be voted on in September.

With only 12 legislative days until a government funding deadline, the focus could soon turn to keeping the government running.

CNN’s Lauren Fox contributed to this report.