Sex and the City star Cynthia Nixon has lost out on her bid to become Governor of New York state, vowing to "keep fighting" for what she believes in.

Nixon lost out on the Democratic Party nomination in Thursday's primary to Andrew Cuomo, who has secured it for the third term.

Following her defeat, Nixon, whose policies included legalising marijuana and abolishing federal body ICE, who identify and remove immigrants from the US, took to Twitter and urged her supporters to keep fighting for the change they want to see.

Nixon (right) with in the Sex and the City movie with her co-stars Kristin Davis (left) and Kim Cattrall

"This is an incredible moment for progressives, but it's not just a moment - it's a movement, and this movement is only growing stronger," she said.

"Our numbers show that the younger you are, the more likely it is that you voted for me today. I'm particularly proud of that fact, and it gives me so much hope for the future of our party and our country.

"The generation coming of age in Obama and Trump's America is one of the most progressive generations in history. You are going to change America - and for the first time in our history create a nation that finally belongs to all of us.

"This is not a time to settle for the way things are, or sit back and hope for things to change. This is a time to fight. As long as New York remains the single most unequal state in the country, we will keep fighting."

Nixon also thanked her supporters saying: "Thank you all for believing and fighting and leaving it all on the field. We started something here in New York, and it doesn't end today. This is just the beginning. And I know that together, we will win this fight."