Harvey Milk enlisted in the United States Navy in 1951 and worked as a diving instructor in San Diego.

He had served for four years when his superiors found him in a park known among gay men, his nephew Stuart Milk said on Monday. Harvey Milk was questioned about his sexuality and forced to resign.

Now a naval ship that honors Mr. Milk is closer to becoming a reality.

The U.S.N.S. Harvey Milk, a fleet oiler named for the slain gay rights leader and first openly gay elected official in a major American city, was celebrated on Friday as the first piece of steel was cut to build the vessel in San Diego.

When completed, the ship will be used to replenish fuel to other Navy ships at sea and jet fuel for aircraft on aircraft carriers, the Navy said. As the ship travels the world, it will help educate people about Mr. Milk’s legacy of L.G.B.T. rights, said his nephew, who noted the ship illustrates how things have changed in the military.