Turkish President Recep Tayyip Erdogan lifted his opposition to Sweden and Finland joining NATO after crunch talks ahead of Wednesday's NATO summit, in return for written security guarantees.

Ankara immediately put the new agreement to the test, with Justice Minister announcing that Turkey would seek the extradition of alleged Kurdish militants and members of a group that Erdogan blames for a failed 2016 coup attempt.

"We will seek the extradition of terrorists from the relevant countries within the framework of the new agreement," Justice Minister Bekir Bozdag was quoted as saying by NTV television.

Bozdag said Ankara would now ask for the extradition of 12 suspects from Finland and 21 from Sweden who were either members of the outlawed Kurdistan Workers' Party (PKK) or alleged members of a group led by the US-based Muslim preacher Fethullah Gulen.

The PKK, which has been waging an insurgency against the Turkish state since 1984, is blacklisted by Turkey, the EU and the United States.

Gulen, a former ally of Erdogan, denies charges of plotting the 2016 coup attempt.

The three-way memorandum signed on Tuesday says that Finland and Sweden pledge to "address Turkey's pending deportation or extradition requests of terror suspects expeditiously and thoroughly".

The two countries also agreed to lift their embargoes on weapons deliveries to Turkey, which were imposed in response to Ankara's 2019 military incursion into Syria.

Erdogan's office hailed the agreement, saying Ankara had "got what it wanted".