Anas Sarwar has written to the chair of the Scottish Hospital Inquiry, urging him to call John Swinney and Nicola Sturgeon to give evidence.
On Monday, the Labour leader asked Lord Brodie to reopen evidence sessions about Glasgow’s Queen Elizabeth University Hospital in order to hear from key Scottish Government ministers.
Sarwar has previously accused the inquiry of failing to properly examine political decision-making.
Sarwar has called for the inquiry to be expanded.
Earlier this month, NHS Greater Glasgow and Clyde admitted there was likely a "causal connection" between infections suffered by cancer patients and "the hospital environment, in particular the water system".
Sarwar wrote: “NHS Greater Glasgow and Clyde claim that they were under pressure to open the Queen Elizabeth University Hospital (QEUH) before it was ready.
“After the inquiry hearing concluded, the health board put out a public statement attempting to clarify that this pressure was internal, but it is still unclear who applied this internal pressure, why they did so, and if it was due to external pressure that they themselves were under.”
He added: “I believe for the purposes of transparency and clarity that this should include oversight and communication from the Scottish Government to the Board.
“Only by scrutinising the role and conduct of Scottish Ministers and the political decision making related to the hospital will the full picture of what occurred be obtained.”
Sarwar said that Lord Brodie should call Sturgeon, who was First Minister at the time of the hospital’s opening in 2015, well as then-Finance Secretary John Swinney and then-Health Secretary Shona Robison.
Sarwar added: “I appreciate that reopening public evidence sessions would be an extraordinary step but I believe that it is the best route to securing the answers that families and staff need and ensuring that your report, and the public, are able to account for this vital component in the scandal.”
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Sturgeon has denied pressuring NHS Greater Glasgow and Clyde to open the hospital early.
Late last week, she said: “Any suggestion that I applied pressure for the hospital to open before it was ready or that I had any knowledge of safety concerns at that time are completely untrue.”
Asked by opposition MSPs to clarify if the Scottish Government had pressured the health board, Swinney said: “The direct answer to that question is no.”
Closing statements from core participants were submitted last weekend, and Lord Brodie is drawing up his final report.