The Scottish Conservative leader said she wanted to act on her proposals, made during the election campaign, to create a new "Parliament with teeth".
Conservative suggestions include a plan to ensure the conveners of certain committees come from opposition parties, and for opposition party spokesmen and women to get greater opportunity to question Government Ministers.
Ruth said the Scottish Conservatives now wanted to consult with other opposition parties in the coming days to form a consensus on the best way forward.
She said: "I said during the election campaign that we would press for a parliament with teeth. Before the new parliament gets underway, we have an opportunity to act on that.
"Too often during the last parliament, bad laws were swept in thanks to the SNP majority. Now they are a minority administration, it puts parliament back in control.
"Some simple reforms now need to be considered – and I want all opposition parties to find common cause in putting those forward.
"We can hold the SNP in check – and ensure better government and a stronger Scotland as a result."