Tuesday's update came a week after several hostages, including Americans, were released.
[Ads /]
Among those hostages set free was Adrienne "Aviva" Siegel, the wife of North Carolina native Keith Siegel, who Budd first raised awareness about on the Senate floor a month ago.
In a conference call that Budd's office recorded Tuesday, the Republican senator vowed to continue pressing Qatar to lean on Hamas for the release of all remaining hostages.
"Well, they've tried to play the middle and they are an ally," Budd said. "They do host U.S. forces over there. We've had a long-term relationship but in this regard, it's very unfortunate that you play the middle with somebody who is sheer evil, and that's Hamas.
[Ads /]
"And so, there's really no excuse to be hosting them at this point when they showed their true colors two months ago," Budd added.
Budd declined to comment about communication he's had with the Siegel family -- or intelligence that might shed light on Keith Siegel's location and condition.
Budd's office said it believes there are still nine Americans being held by Hamas.