The Turkish side is being led by Kasım Çiçek, the director general of Foreign Relations and the European Union at the Justice Ministry.
The two-day talks are being held in the Turkish capital Ankara.
Last week, Turkish Justice Minister Bekir Bozdağ said: "We expect Sweden and Finland to extradite FETÖ (Gülenist Terror Group) and PKK (terror group) members to Türkiye within the scope of the NATO agreement."
President Recep Tayyip Erdoğan had warned recently that Türkiye will not ratify Sweden and Finland's NATO membership bids unless the two Nordic countries "keep their promises.”
For Sweden and Finland to become NATO members, their applications must be ratified by all 30 NATO members. So far, 28 have already done so – only Türkiye and Hungary have votes still pending.
Ankara is "monitoring" Stockholm and Helsinki's efforts in fulfilling their commitments and "can not make concessions" on the issue of fighting terrorism, Erdoğan said.