Ankara has objected to Sweden and Finland joining the Western defence alliance, holding up a deal that would allow for a historic enlargement following Russia’s invasion of Ukraine.
Mr Erdogan’s latest comments indicate that his opposition continues.
He highlighted the activities of the Kurdistan Workers’ Party as part of his country’s objection to the two countries joining the security bloc.
The group known as PKK has waged a 38-year insurgency against Turkey that has led to tens of thousands of deaths. It is designated a terrorist entity by the United States and the European Union, including Sweden and Finland.
However, the West’s attitude to the PKK’s Syrian wing, the People’s Protection Units, or YPG, has caused acrimony between Ankara and other Nato members.
The YPG forms the backbone of the forces involved in the US-led fight against the Islamic State group.
“Turkey maintains that the admission of Sweden and Finland entails risks for its own security and the organization’s future,” President Erdogan wrote in an article published by The Economist on Monday.
Referring to the central tenet of Nato’s mutual defense policy, he added: “We have every right to expect those countries, which will expect Nato’s second-largest army to come to their defence under Article 5, to prevent the recruitment, fundraising and propaganda activities of the PKK."
All Nato members must approve the two Nordic nations’ bids to join the alliance, which were propelled by Russia’s invasion of Ukraine.
Turkey has said it won’t allow their accession unless steps are taken, but Nato leaders are looking to the Nato summit in Spain in late June as the chance for the historic expansion.
Mr Erdogan reiterated calls for Finland and Sweden to extradite people Ankara suspects of terrorist activity and to support "the anti-terror operations of Nato members”.
He also said arms embargoes were “incompatible with the spirit of military partnership."
Sweden and Finland were among countries to impose defense export restrictions on Turkey following its 2019 incursion into northeast Syria that aimed to drive back the YPG.
In recent days, Mr Erdogan has promised a further cross-border operation against the group.
The president set out Turkey’s role in “arguably the greatest military alliance in history” since it joined in 1952 and called for other Nato members to persuade Sweden and Finland to change their positions.
“Where Sweden and Finland stand on the national security concerns and considerations of other countries, with which they would like to be allies, will determine to what extent Turkey would like to be allies with those states,” he added.