Police have scaled back the search for a man who has been missing since a boat capsized in waters off Melbourne on Friday night.

Authorities were told a small vessel carrying two men was about a kilometre from the Mornington Pier in Port Phillip Bay when it got into trouble at about 11:15pm.

One of the men was rescued by another boat without serious injuries.

But the search for the other man, Sam Fowler, continued over the weekend.

Both men are believed to be in their 20s.

The families involved in the search on Monday issued a statement thanking emergency responders and mourning the "loss of Sam Fowler".

"On behalf of the Fowler, Mitchell, and Elvey families, we extend our heartfelt thanks to everyone who has offered love and support during this devastating time," the statement said.

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