Turkey and Hungary are the only Nato members still to ratify the bids of the Nordic nations, which must be accepted by all 30 existing members of the military organisation.
Ankara had suspended negotiations with Sweden and Finland in outrage after protests in January that included the burning of the Quran outside its embassy in Stockholm.
A new round of talks announced by Turkey last month will take place at Nato headquarters in Brussels on Thursday.
Stoltenberg insisted on a visit to Sweden that getting the memberships finalised was “a top priority”.
“We are making progress,” he said at a press conference with the Swedish prime minister.
Stoltenberg said Stockholm “has delivered” on a deal with Turkey inked last year that was meant to pave the way to Nato membership.
“The time has come to finalise the ratification process,” he said.
Two previous rounds of the tri-party Nato talks were attended by foreign ministry officials and focused on a specific list of Turkish demands, which include the expulsion of dozens of mostly Kurdish suspects.
Stoltenberg refused to speculate on the results of the fresh negotiations this week.
Turkey has raised the prospect of accepting Finland without letting Sweden’s application through. Nato officials are sceptical about splitting up the bids, but increasingly accept Helsinki may join first.
Turkish President Recep Tayyip Erdoğan has dug in his heels on Sweden as he heads into a close presidential election in which he is trying to energise his nationalist electoral base.
Stoltenberg said that he also expected Hungary’s parliament to complete the process of ratifying the applications “shortly”.
That came as a visiting Hungarian parliamentary delegation said Swedish politicians need to stop spreading “lies” about Budapest and the rule of law.
Budapest is still expected to vote in favour of both countries joining the alliance “in the coming weeks”, the deputy speaker of the Hungarian parliament Csaba Hende told reporters in Stockholm.
Both Finland and Sweden dropped their decades-long policies of military non-alignment and applied to join the alliance last May in the wake of Moscow’s invasion of Ukraine.