Turkish President Recep Tayyip Erdogan has said he intends to forward the ratification of Sweden's Nato bid to Parliament when it reopened in the autumn.
But Mr Erdogan said he expected Stockholm to take some steps against terrorism in return.
Turkey has resisted Sweden's ratification for months, accusing the country of doing too little against people it sees as terrorists, mainly members of the outlawed Kurdistan Workers Party (PKK).
However, Mr Erdogan agreed to forward Sweden's Nato accession bid to parliament in an unexpected turn on Monday.
He told a news conference after the Nato summit in Lithuania that Sweden would provide a road map to Turkey over the steps it will take before the ratification is sent to Parliament.
Turkey's Parliament closes at the end of the week and will reconvene in October.
"When it reopens, I believe our parliament Speaker will bring this forward among international agreements. The primary place of approval is the parliament, then it will come to me for approval," Mr Erdogan said.
"We want this process to end as soon as possible."
Sweden and Finland applied for Nato membership last year in response to Russia's invasion of Ukraine, abandoning policies of military non-alignment that had lasted through the decades of the Cold War.
Day two of Nato summit in Lithuania - in pictures
Mr Erdogan said Stockholm would also support updating Turkey's customs agreement with the EU, and visa-free travel.
Turkey expects an EU reform group to be revived after Ankara approves Sweden's Nato membership as it seeks to enter a new period of improved ties with the West, a senior Turkish official told Reuters on Tuesday.
Meanwhile, a senior official told Reuters on Wednesday that Mr Erdogan's government would hold talks with its parliamentary ally on ratifying Sweden's accession, after the Nationalist Movement Party appeared to take a negative view on the issue.
MHP leader Devlet Bahceli said on Tuesday that Sweden had failed to distance itself from terrorism, but added that Mr Erdogan would make the final call about Sweden's membership bid.
Mr Erdogan's Justice and Development Party, or AKP, relies on the MHP for a parliamentary majority, which is required to push through the ratification.
Other parties in parliament have not said whether they would support the move.
"There will be contacts with the MHP either by the president or by high levels of the government," the official said.
"Bahceli's comments are not fully compatible with the steps that have been taken so far.
"The behind-the-scenes developments and the reasoning for the decision that was taken will be relayed to Bahceli and other MHP executives."
Ankara also expects the lifting of some "implicit" economic restrictions, including embargoes and restrictions of arms trade, by Sweden and other EU and Nato countries, the official said.
A statement issued by Turkey and Sweden on Monday said Stockholm had reaffirmed that it would not provide support to the Kurdish groups and would actively support efforts to reinvigorate Turkey's EU accession process.
The PKK is considered a terrorist organisation by Turkey, the EU and the US.
