Finance secretary Kate Forbes was urged to put her own job on the line if the latest delivery deadline is not met.
It comes after it emerged there were 237 outstanding faults with the ferries as of March.
The vessels, the Glen Sannox and the as-yet-unnamed hull 802, are at least £150 million over budget and five years late.
One is destined for the Arran route and the other will serve Skye, North Uist and Harris.
There is ongoing controversy over their botched construction at the Ferguson Marine shipyard in Port Glasgow.
Ms Forbes said the Glen Sannox will be delivered between March and May 2023 and hull 802 will be delivered between October and December.
But Tory MSP Jamie Greene, who represents West Scotland, said: "I want a cast-iron iron guarantee – so do our islanders – that vessel 801 [the Glen Sannox] will be in service by this time next year, and vessel 802 will be in service by the autumn of next year."
Speaking in Holyrood, he added: "Let me ask the Cabinet secretary, on a confidence level of one to ten, how confident is she that the Glen Sannox will be sailing passengers to Brodick by this time next year?
"And in the spirit of taking responsibility, will she put her job on the line if it doesn't?"
Ms Forbes said she represented a community – Skye, Lochaber and Badenoch – which was set to benefit from one of the ferries.
She said there were 237 owner observation reports [OORs] in March and "good progress is being made in clearing those issues".
Of these, 119 are assessed as "category one", while the rest are "minor snagging".
Ms Forbes said: "Within the 119, there are engineering solutions for 83, leaving 36 that are still being worked on.
"Solutions are expected progressively without delays or impacts on the programme."
She added: "Solving all these issues is critically important, it's part of the programme and I think we've got the best people on the ground to do that."
Mr Greene responded: "We do have good people, but what we don't have is an answer.
"No cast-iron guarantee and once again no one in the SNP is willing to take full responsibility for the delivery of this project or the delivery of those vessels."