The bank is set to shut 11 branches in north Wales by September, including two at Llangollen and Corwen.
Clwyd South AM Ken Skates, who has set up the meeting for later this month, said Corwen would be left without any banks if the branch closed.
Bank bosses said they had made the "difficult decision" due to several factors, including usage.
A politician is to meet Natwest bank bosses in a bid to save two branches from closure in Denbighshire.