Ankara has accused the two Nordic nations of providing safe haven to outlawed Kurdish militants it deems “terrorists”.
“I recognise your concerns,” Stoltenberg told a joint news conference with Turkish Foreign Minister Mevlut Cavusoglu in Istanbul.
He said Finland and Sweden were keen to work closer with Turkey to fight “terrorism”.
“It’s also in their interest,” he said.
“It’s time to welcome Finland and Sweden as full members of Nato. Their accession will make our alliance stronger and our people safer.”
Cavusoglu in turn said that that Turkey believed that Sweden’s new government was more committed to meeting Turkey’s demands. The most important thing was that the actions laid out in the agreement reached in June between Turkey, Sweden and Finland were taken in full, he said.
Both countries dropped decades of military non-alignment and scrambled to become Nato members in May, after Russia invaded Ukraine.
But Turkish President Recep Tayyip Erdogan threatened to block their bids, seeking concessions.
In June, Turkey, Sweden and Finland struck a deal which included provisions on extraditions and sharing information.
“Finland and Sweden have delivered on their agreement to Turkey,” Stoltenberg said. “They have become strong partner in our joint fight against terrorism in all its forms and manifestations,” he added.
“And they are clearly committed to long-term engagement with Turkey to address your security concerns.”
To date, all but Turkey and Hungary of the 30 Nato member states have ratified the accession of Sweden and Finland.
New members to the alliance require unanimous approval
Cavusoglu said Stockholm took some steps including the removal of restrictions standing in the way of arms sales to Turkey but added “it’s not possible to say” the July agreement was fully implemented.
“We don’t intend to harm NATO or block its enlargement … we want to see concrete steps,” he said.
Ankara is “more hopeful” that Sweden’s new government will address Turkey’s concerns, Cavusoglu added.
“We knew that the outgoing government could not do much. The new government is decided and the new prime minister is going to visit our country next week,” Cavusoglu said.
During his visit to Istanbul, Stoltenberg met Cavusoglu, Turkey’s defence minister Hulusi Akar, and other politicians.
“Finland and Sweden have significantly increased their cooperation with Turkey on combatting terrorism,” Stoltenberg said.
On Friday, Stoltenberg will hold a one-on-one meeting with Turkey’s president, Recep Tayyip Erdogan.
Sweden’s new Prime Minister Ulf Kristersson will visit Ankara next Tuesday for further talks.