Many lawmakers plan to attend funerals for those killed in last week's shooting.
The Senate is expected to vote on going to conference with House lawmakers later this week.
"The United States is the only advanced country where this type of mass violence occurs."
"It's an important moment for the country," he said ahead of a procedural vote.
A push to pass fast-track trade legislation faces a test vote in the Senate.
The bill has some bipartisan support, but faces an all-but-certain Obama veto.
Sen. Ben Sasse (R-Neb.) was the lone "no" vote.
The Alabama senator says Republicans "have a second chance" on trade.
The bank is set to expire at the end of the month.
The panel said media reports have "directly impacted the committee's investigation."