Stoltenberg is set to fly to Ankara on Thursday and also head to the region devastated by the quakes last week.
Turkey's Nato counterparts have been pleading with Ankara to sign off on Sweden and Finland's stalled bid to become members.
Parliaments in all 30 members of the military alliance must formally ratify Finland and Sweden before they can be admitted. Turkey and Hungary are the only two Nato members not to have done this.
Ankara has suggested it could greenlight Finland's bid without accepting Nordic neighbour Sweden into the alliance.
Stoltenberg said the ball was in Turkey's court to move forward with the process.
"It is for Turkey to decide whether they ratify both and I have recommended that," Stoltenberg said.
"The sequencing is not the most important thing. The most important thing is that both Finland and Sweden and soon become members of the alliance and I'll push hard for that."
Finland, which shares a long border with Russia, and Sweden dropped decades of military non-alignment and applied to join Nato in May last year in response to Moscow's invasion of Ukraine.
Turkey has been upset by Sweden's refusal to extradite dozens of suspects that Ankara links to outlawed Kurdish fighters and a failed 2016 coup attempt.
Ankara reacted with fury to a decision by the Swedish police to allow a protest at which a far-right extremist burned a copy of the Koran outside the Turkish embassy in Stockholm last month.
Diplomats at Nato are still hopeful that Turkish President Recep Tayyip Erdogan could wave through the ratifications if he secures re-election at the polls in May.
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