"As long as Sweden continues to allow branches of terrorist organizations in Turkey to walk freely in Sweden, on the streets of Stockholm, we cannot look positively on Sweden's membership in NATO," Erdogan said.
The Swedish government hopes to be a full member of the NATO summit in Lithuania on 11-12 July.
"We are not ready for Sweden right now," Erdogan added in the interview with CNN.
"Because a NATO country should be in a strong position when it comes to fighting terrorism.
New ballot
No winner could be declared in last weekend's presidential elections in Turkey. Instead, a new round of elections awaits on 28 May.
"Right now, we shouldn't think anything is happening in this process. Right now, Turkey is engaged in domestic politics, Prime Minister Ulf Kristersson (M) said earlier this week.
Although Kristersson has not given up hope of Swedish NATO membership this summer, he noted that time is becoming increasingly short.
"Of course time is shrinking," he said.
SVT News has contacted Foreign Minister Tobias Billström (M), who has announced that he is not able to comment on the resignation at the moment.
That means NATO membership
Protection
32 sec
Obligations
36 sec
Who decides?
31 sec
Application
32 sec