Senate Majority Leader John Thune (R-S.D.) said Monday he still expects the chamber to hold an initial vote on a closely watched bill to regulate cryptocurrency before its planned recess later this week.

“I think market structure we’ll get a vote on. Whether we can get on it or not, we’ll see,” Thune told reporters, adding that the Senate has “a bunch of stuff we have to finish” in a tight window.

Backers of the bill, known as the Clarity Act (H.R. 3633), have pushed for the Senate to hold an initial procedural vote to close debate on …