Turkish President Recep Tayyip Erdogan on Monday demanded that Nato complies with Ankara's conditions as he renewed his threat to "freeze" the bids of Sweden and Finland to join the military alliance.
During a Nato summit in Madrid at the end of June, Mr Erdogan accused the two countries of providing a haven for outlawed Kurdish militants and called on them to "do their part" in the fight against terrorism.
"I want to reiterate once again that we will freeze the process if these countries do not take the necessary steps to fulfil our conditions," he said on Monday, the eve of three-way summit with Russia and Iran.
"We particularly note that Sweden does not have a good image on this issue."
This month Nato began the accession procedures for Sweden and Finland after a deal was struck with Turkey, which had blocked them from joining.
Mr Erdogan has accused both countries of being havens for Kurdish militants, specifically the outlawed Kurdistan Workers' Party (PKK) he has sought to defeat, and for promoting "terrorism".
In Washington, State Department spokesman Ned Price did not speak directly of Mr Erdogan's remarks but referred to Turkey's approval during the Nato summit to the new memberships.
"Turkey, Finland, Sweden — they signed a trilateral memorandum in Madrid to set this process in motion," Mr Price said.
"The United States will continue to work with those three countries to see to it that this accession process and ratification — here and around the world — is as swift and efficient as it can possibly be."
Mr Erdogan is due to board a plane to Tehran on Monday evening for talks on Tuesday with Russian President Vladimir Putin and Iranian President Ebrahim Raisi, from whom he hopes to receive approval for armed intervention in north-west Syria.
Ankara has been threatening since late May to launch an operation to create a 30-kilometre "security zone" along its border to tackle Kurdish fighters waging an insurgency against the Turkish state.
Tehran and Moscow have already expressed their opposition to such an offensive.
Russia, Turkey and Iran are all major players in the war that has ravaged Syria since 2011, with Moscow and Tehran supporting the regime of Bashar Al Assad and Ankara supporting rebels.