Turkey's President Recep Tayyip Erdogan, who has objected to Sweden and Finland joining Nato, held phone calls with the leaders of the two countries on Saturday and discussed his concerns about "terrorist groups".
Turkey says Sweden and Finland harbour people linked to the Kurdistan Workers' Party (PKK) insurgent group and followers of Fethullah Gulen, whom Ankara accuses of orchestrating a 2016 coup attempt.
Mr Erdogan told Sweden's Prime Minister Magdalena Andersson that Ankara expected concrete steps would be taken to address its concerns, the Turkish presidency said.
He also said an arms sales embargo imposed on Turkey after its incursion into Syria in 2019 should be lifted.
Ms Andersson said she appreciated the call and that Sweden hoped to strengthen bilateral relations with Turkey.
"I emphasised that Sweden welcomes the possibility of co-operation in the fight against international terrorism and emphasised that Sweden clearly supports the fight against terrorism and the terrorist listing of the PKK," she said.
In a separate call, Mr Erdogan told Finnish President Sauli Niinisto that failing to deal with organisations that posed a threat to a Nato ally would not suit the spirit of alliance, Ankara said.
Mr Niinisto said he held "open and direct" talks with Mr Erdogan and agreed to continue close dialogue.
Turkey surprised its Nato allies last week by objecting to the two countries' accession to the military alliance, but western leaders have expressed confidence that Ankara's objections will not be a roadblock for the membership process.
All 30 Nato states must give their approval before a new member can be admitted and thus benefit from the collective-security guarantee.