(CNN) Deputy Attorney General Rod Rosenstein expressed confidence Monday in Attorney General Bill Barr's judgment in overseeing the special counsel's Russia investigation, as Democratic lawmakers gear up to pressure the Justice Department to turn over Robert Mueller's findings.

The timing for when Mueller finally delivers his report to Barr continues to be a moving target , and Rosenstein demurred when asked about the "process."

Under the special counsel regulations, Mueller must detail why he did or did not opt to prosecute different matters in a confidential report to the attorney general at the end of investigation -- but that report is not required to be made public.

"What's the attorney general going to do? You have to ask him that question," Rosenstein joked at an event hosted by the Center for Strategic and International Studies.

"I think Attorney General Barr is going to make the right decision," he added. "We can trust him to do that. He has a lot of experience with this. ... I think we can count on him to do the right thing."

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