US President Donald Trump has said he will next week nominate a woman to replace the late US Supreme Court Justice Ruth Bader Ginsburg, escalating a political row with the Democrats over her successor weeks before the presidential election.

"I will be putting forth a nominee next week. I could say most likely it would be a woman. I think I can say that. If somebody were to ask me now I would say that a woman would be in the first place," Trump told supporters at an election rally in North Carolina on Saturday.