He said Sweden has done what is necessary to secure Turkey’s approval for membership.
“I have said that time has come to bring to an end the ratification process for Sweden,” Mr Stoltenberg told Swedish newspaper Aftonbladet.
Sweden and neighbour Finland, which shares a border with Russia, both applied for Nato membership in May last year after the Russian invasion of Ukraine.
Nato members must give unanimous consent to new applicants and Turkey has demanded both countries crack down on groups it considers to be terrorist organisations and extradite people suspected of terror-related crimes.
Most of Turkey's demands have involved Sweden’s relationship with the Kurdish diaspora.
Swedish Prime Minister Ulf Kristersson said on Sunday that it cannot accept some of those demands.
“Turkey has confirmed that we have done what we said we would do, but it also says that it wants things that we can't, that we don't want to give it,” Mr Kristersson said.
“We are convinced that Turkey will make a decision, we just don't know when.”
Mr Kristersson said it would depend on Turkey's internal politics and “Sweden's capacity to show its seriousness”.
“Legislation banning participation in terrorist organisations is being implemented, and Turkey is known to name individuals it wants extradited,” he added.
“It is also known that Sweden has legislation that is clear and means that it is up to the courts. We also do not extradite Swedish citizens to any country.”
He was speaking at the People and Defence conference, a meeting of Swedish foreign policy and security experts. Mr Stoltenberg was also there.
There was no immediate reaction from Turkey after either the Swedish comments on Sunday or Nato comments on Monday.
Sweden and the US have begun negotiations to form deeper security ties in the form of a defence co-operation agreement, the Swedish government said on Monday.
It will create a legal framework for the presence of US forces in Sweden and allows for closer bilateral co-operation than facilitated by Nato membership, the Swedish defence ministry said.
“The US is Sweden's most important security and defence partner, both bilaterally and within Nato,” the ministry said.
Last month, Turkish Foreign Minister Mevlut Cavusoglu said Sweden was not even “halfway” through fulfilling the commitments it made to secure Ankara’s support.
That came after a Swedish court ruled against extraditing a man wanted by Turkey for alleged links to a 2016 failed coup.