A House Republican introduced a resolution Thursday encouraging special counsel Robert Mueller to end his year-long investigation unless he can prove he's made progress examining the possible links between Russia and the Trump administration.

“The Mueller investigation has dragged on for nearly a year at a cost of tens of millions of dollars without producing a shred of evidence of collusion — the matter it was tasked with investigating in the first place. I expect a valid progress report within the next 30 days or the investigation should be terminated,” Rep. Todd Rokita, R-Ind., said in a statement.

[Also read: Ex-Trump aide Michael Caputo: Mueller has 'entire campaign’s texts']

Rokita, a former state secretary, added that even federal officials must be held accountable for their actions, though Mueller has not been alleged of any wrongdoing related to the probe.

“No one in government should be without accountability, and for many Americans, this investigation looks more like an attempt by the Washington elite to destroy President Trump with innuendo, leaks, and baseless allegations than to provide justice," he said.

Even with Republicans in control of the House, it seems unlikely Rokita's resolution will be brought up, as House GOP leaders have said Mueller needs to be able to finish his work.

[Related: Eric Holder predicts the Mueller investigation will be a 'two-year case']

Rokita is running this year for Sen. Joe Donnelly's, D-Ind., seat, but a recent poll says Donnelly is likely to hold onto it.

This week, Trump hired former New York City Mayor Rudy Giuliani as his personal attorney to deal with the Mueller probe. His longtime personal lawyer Michael Cohen is under investigation for issues connected to his unrelated business and a payment he gave porn star Stormy Daniels prior to the election.