"Given that we are talking about the first potential meeting between the two heads of state in the current circumstances, it certainly has a special significance," Peskov told Russian journalist Pavel Zarubin.
Trump can come to Russia at any time when his visit is agreed upon, the spokesman added.
Peskov further said that the telephone conversation between the two presidents was a powerful signal of the start of a dialogue on peace.
"This is a powerful signal that we will now try to solve problems through dialogue, and will talk about peace, not war," Peskov told Zarubin.
The meeting between the presidents would have required less preparation if the countries had a regular dialogue, the spokesman noted.
"If we were in the mode of regular dialogue, in the mode of normal interstate relations, it would probably require less preparation," Peskov said.
The spokesman added that Trump's statements suggest that he supports the "no war, we need peace" position.
"What happened with the previous [US] administration - no dialogue, war until the end. This was the official position of the previous administration. Judging by President Trump's statements: we solve problems through dialogue, no war, we need peace. This stance, in theory, should appeal more to any sane person or state," the spokesman said.