US President Joe Biden has backed an agreement that would allow Sweden and Finland to join NATO and help achieve agreement behind the scenes of the Nordic countries with Turkey, said a senior US official.

Turkey has stopped opposing Finland and Sweden joining NATO before the Alliance's annual summit in Madrid.

The official said Biden had spoken with the Turkish president earlier on Tuesday Recep Tayyip Erdogan for NATO at the request of both countries.

He said the agreement would allow the 30-member alliance to expand and represent a "significant change in security".

Turkey has not insisted that its demands for advanced US warplanes be included in the negotiations, the official said.

Biden and Erdogan are expected to meet on the sidelines of the summit.