Melania is set to become first lady in January when her husband Donald Trump takes up the US presidency.
Gigi imitated her European accent, also making reference to claims Melania copied a speech made by Michelle Obama.
"I removed or changed anything in the script that I felt took the joke too far, and whether or not you choose to see it, what remained was done in good humour and with no bad intent," Gigi wrote.
"I too have been the centre of a nationally televised comedy skit that poked fun at my actions, and was able to find the humour in it.
"I believe Melania understands show business and the way shows are written and run."
Her co-host, Jay Pharoah called for people to "leave Gigi alone" and shared a message of support on his Instagram feed.
"Everybody pump on the brakes one minute," he wrote.
"Over the last eight years the beautiful Michelle Obama has been the victim of excessive slurring."
Reaction on the night to Gigi`s imitation of Melania was mixed.
Other artists also used the event to pass comment about the forthcoming Trump presidency.
Green Day turned a performance of their track Bang Bang into an anti-Trump song.
"No Trump! No KKK! No Fascist USA!" Green Day frontman Billie Joe Armstrong shouted to the audience.
