Pro-government Turkish media lauded a deal to allow Finland and Sweden to join NATO as a triumph for President Tayyip Erdogan, saying on Wednesday he had wrested concrete gains from the West in the country's fight against terrorism.

The 11th hour agreement on Tuesday, which caught many by surprise, lifted Ankara's veto over the Nordic states' membership bids. It ended a weeks-long dispute that tested the defence alliance's unity against Russia's invasion of Ukraine ahead of this week's NATO summit in Madrid.

"President Erdogan's Madrid Victory," said a Sabah newspaper headline, above a photo of him standing next to NATO Secretary-General Jens Stoltenberg at the centre of a group photo after the accord was signed.

"Erdogan's decisiveness and leadership vision won acceptance for all of Turkey's arguments in the fight against terrorism," the paper said.

The pro-government papers echoed a note circulated by Erdogan's office before the memorandum was released in Madrid. The much smaller number of independent and anti-government media gave little immediate coverage or comment on the deal.

Meral Aksener, head of Turkey's opposition IYI Party, said the deal was unacceptable and that Ankara would have no "NATO card" to play if the three-way mechanism did not work.

"This signature that the government gave without any concrete developments from Sweden and Finland is unfortunately a compromise that is not in line with the interest of our country," she told MPs from her party in parliament.

'NINE GUARANTEES'

The pro-government Aksam newspaper listed the elements of the agreement noting it would establish a monitoring mechanism sought by Ankara. "Nine guarantees for Turkey," it said.

The two Nordic nations pledged not to support groups which Ankara deems terrorists and committed to prevent activities of the militant Kurdistan Workers Party (PKK) and its affiliates.

Notably, the statement said Finland and Sweden would not support the Syrian Kurdish YPG militia, which Ankara says is such an affiliate.

Turkey's Western allies designate the PKK as a terrorist group but not the YPG, which is a key element of the Kurdish-led coalition that the United States largely relied on to fight Islamic State.

The PKK launched its insurgency against the Turkish state in 1984. More than 40,000 people have been killed in the conflict.

"Two strongholds of terrorism fall in Europe," said the Yeni Akit newspaper. "Sweden and Finland accepted Turkey's demands".

The agreement also said Finland and Sweden would address Turkish extradition requests for suspected militants thoroughly and they would both lift restrictions on selling weapons to Turkey.

"Turkey got what it wanted at the table," said Milliyet newspaper, adding PKK suspects would be extradited to Turkey. However the deal said only that the Nordic states would "address" Turkey's requests "expeditiously and thoroughly".

Finnish President Sauli Niinisto noted the memorandum did not list individuals for extradition.