"Seeing a Pride flag waving so proudly outside your house every day has given me the courage to come out to my family."
The decision in California is a rejection of President Donald Trump's policy prohibiting U.S. diplomatic missions from flying the rainbow flag.
Pastor E.W. Jackson, a Baptist minister, praised the Trump administration for rejecting requests from U.S. embassies to fly the gay pride symbol on their flagpoles this month.
"When it comes to the American flagpole and American embassies and capitals around the world, having the one American flag fly is the right decision," Pence said.
Reverend Paul Kalchik's actions sparked protests from LGBT activists last week.
The monument will honor the LGBT community, victims of the Pulse nightclub shooting and 'all victims of hate, intolerance and violence.'