"For as long as Tayyip Erdogan is the head of the Republic of Turkey, we definitely cannot say 'yes' to countries which support terrorism entering NATO," he was cited as telling reporters on his return from a trip to Azerbaijan on Saturday.
Two sources previously told Reuters that Wednesday's talks with Finnish and Swedish delegations made little headway and it was unclear when further discussions would take place. All 30 NATO members must approve plans to enlarge NATO.
Turkey challenged the bids from Sweden and Finland on the grounds that the countries harbour people linked to the Kurdistan Workers Party (PKK) militant group and others it deems terrorists, and because they halted arms exports to Ankara in 2019.
"They are not honest or sincere. We cannot repeat the mistake made in the past regarding countries that embrace and feed such terrorists in NATO, which is a security organisation," he said.
Sweden and Finland have said they condemn terrorism and welcomed the possibility of coordinating with Ankara.
"Diplomatic efforts are ongoing. We decline to comment further at this moment," Swedish Foreign Minister Ann Linde said in an emailed comment to Reuters following Erdogan's latest statement.
Erdogan also said Turkey wanted to see an end to the war between Russia and Ukraine as soon as possible, but that the situation was becoming more negative each day.
"On Monday, I will have phone calls with both Russia and Ukraine. We will continue to encourage the parties to operate channels of dialogue and diplomacy," he said.