Earlier in the day, Ukrainian President Volodymyr Zelenskyy called Putin’s proposal an "ultimatum."
"It is surely a misunderstanding, it is exactly a peace initiative," Peskov told the Izvestia newspaper.
The spokesman called Putin’s proposal a "real peaceful" initiative.
"It talks about further discussion of security guarantees and so on and so forth, so it is a comprehensive, very deep and constructive proposal," the spokesman said.
The situation today is different from 2022 "de facto and de jure," Peskov said, adding that it is necessary to take into account entry of new regions into Russia when discussing peace with Ukraine.
Earlier in the day, Zelensky said in an interview with Italian broadcaster Sky TG24 on the sidelines of the G7 summit in Italy that Putin's proposal for Ukraine was no different to Russia's proposals made in previous years.
Putin said at a meeting with top officials of the Russian Foreign Ministry earlier on Friday that in 2022, he had entertained the possibility of allowing Ukraine to keep control over parts of the Kherson and Zaporozhye regions, but added that this possibility expired after the two regions became part of the Russian Federation in September 2022.