Turkish President Recep Tayyip Erdogan has said he believes Russia's leader is seeking an end to the war he began in Ukraine, and that a "significant step" will be made.
He said his impression from recent talks with Vladimir Putin was that he wanted to "end this as soon as possible".
Ukraine has recaptured swathes of its territory this month.
The Turkish leader indicated things were "quite problematic" for Russia.
Erdogan spoke of having "very extensive discussions" with Putin at a summit in Uzbekistan last week.
In an interview with US broadcaster PBS, the Turkish leader said he gained the impression that the Russian president wanted a speedy end to the war.
"He is actually showing me that he's willing to end this as soon as possible," Erdogan said. "That was my impression, because the way things are going right now are quite problematic."
He also said 200 "hostages" would soon be exchanged between the two sides. He gave no further detail of who would be included in such a prisoner swap.
Erdogan has repeatedly sought to mediate during the war, promoting a "balanced" stance for Nato member Turkey, while opposing Western sanctions on Russia.
He helped the UN mediate a resumption of grain exports from Ukraine and said last week he was trying to organize direct ceasefire talks.
Meanwhile, two months after Russian forces seized control over the entire eastern region of Luhansk, Ukraine has reclaimed part of the territory.
Luhansk's Ukrainian leader Serhiy Haidai said Russian forces had retreated from the village of Bilohorivka - but were doing all they could to dig in elsewhere.
President Volodymyr Zelensky said "the occupiers are clearly in a panic".
Earlier this month, Erdogan accused the West of adopting a policy of "provocation" toward Russia and warned that the war was unlikely to end "any time soon".
Last week the Russian leader said he was open to meeting the Ukrainian president, but that Zelensky was not. He told India's prime minister he wanted to end the fighting "as soon as possible".
However, Russia has not given any indication that it is prepared to accept Kyiv's demands for a full withdrawal from Ukrainian territory, including areas seized in 2014.
Crimea was annexed by Russia at the time, and now ex-President Dmitry Medvedev has said that Russian-backed separatists should hold "referendums" on annexing the territories of Luhansk and Donetsk - which are known as Donbas.
President Putin has repeatedly identified "liberation" of Ukraine's Donbas region as Russia's main goal. "Referendums in Donbas are essential," said Medvedev, who is now deputy head of Russia's security council.
Local Russian-backed leaders in Luhansk and Donetsk have also called for urgent referendums, and Ukrainian defense ministry adviser Oleksiy Koptyko suggested they were a "sign of hysteria" in Moscow, as well as an attempt to spur Putin into action.
As well as recapturing much of the Kharkiv region in the north-east, Ukrainian forces have launched a counter-offensive in the southern region of Kherson, forcing its Russian-installed leader to delay a referendum on joining Russia.
Asked by PBS whether Russia should be allowed to keep any territory it had taken since February, and whether that should be part of a peace deal, Mr Erdogan said: "No, and undoubtedly no."
He also said that "lands which were invaded will be returned to Ukraine". It was not clear whether he also included territory held by Russian-backed separatists since 2014.
Asked whether Russia should be allowed to keep Crimea — which it annexed in 2014 — Erdogan said that since then, Turkey had been talking to Putin about returning the peninsula "to its rightful owners" but that no progress had been made.