George Taft, 65, and Ian Catterson, 73, were killed in the incident off the coast of Greenock.
The sinking sparked a major search operation, which led toPolice Scotland said efforts to recover the tugboat would be made in the coming days.
"As our inquiries continue there will be an increased police presence in the area. I thank the local community for their support and understanding." Mr McMillan, who represents Greenock & Inverclyde, also said the incident had left the local community "deeply shocked" and with "many, many questions". She added: "I know there will be a lot of people who would wish to understand what has happened, most of all those who are mourning."
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