Turkey said it would consider supporting Sweden's application if it takes a clearer stance against what it sees as terrorists — mainly Kurdish militants and the organisation it blames for a 2016 coup attempt.
Finland and Sweden signed a three-way agreement with Turkey in 2022 aimed at overcoming Ankara's objections to their Nato membership.
Staffan Herrstrom, Sweden's ambassador to Turkey, was summoned to the foreign ministry on Thursday and Ankara's reaction was conveyed to him, a Turkish diplomatic source said.
“Our expectation that the perpetrators of the incident need to be identified, the necessary processes be carried out and Sweden uphold its promises was emphasised,” the source said.
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Sweden's foreign ministry confirmed the ambassador had been summoned in Ankara, but declined to give details of what was discussed.
Mr Herrstrom was previously summoned in October over “insulting content” about Mr Erdogan on Swedish public service television.
Scenes of protests in Stockholm has been a particular issue mentioned by Turkish authorities in the past, with Mr Erdogan saying members of the outlawed Kurdistan Workers Party (PKK) should not be allowed to parade around Sweden.
On Thursday, footage shared by pro-government Turkish media showed what they said was a protest by PKK members in which they hung a puppet of Mr Erdogan outside the Stockholm city hall. Very few people could be seen in the footage.
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Swedish Foreign Minister Tobias Billstrom said Stockholm condemned the incident but did not refer directly to any country.
“The government protects an open debate about political choices, but strongly distances itself from threats and hatred against political representatives,” he said on Twitter.
“Portraying a popularly elected president as being executed outside City Hall is abhorrent.”
Sweden's Prime Minister said on Sunday that Stockholm was confident Turkey would approve its Nato bid, but would not meet all the conditions Ankara has set.
“That PKK terrorist can challenge the Swedish government at the heart of Stockholm is proof that the Swedish authorities have not taken necessary steps against terrorism,” the Turkish presidency's communications director, Fahrettin Altun, said on Twitter.