He said this, commenting on the statement of the US National Security Adviser Jake Sullivan about his readiness for dialogue with Russia on the creation of a new nuclear arms control system.
"This is an important and positive statement by Mr. Sullivan. Of course, we hope that it will be supported by de facto steps through diplomatic channels. Then it will be possible to consider the proposed formats of dialogue," Peskov said.
According to him, Russia remains open to dialogue.
"We think this is extremely important, but we must first understand how this proposal is formulated," he added.
Peskov stressed that "in such important and sensitive issues, it is very difficult to focus on statements in the press."
"Especially when we are experiencing an acute deficit of mutual trust in our bilateral relations," he explained.
Earlier, the assistant to the Russian president, Yuri Ushakov, said that the gap in relations between Russia and the United States is not yet visible.
At the same time, he noted that some contacts between Russia and the United States exist - through diplomatic channels or on the topic of the exchange of prisoners, but "from time to time."
On June 2, Assistant to the US President for National Security Jake Sullivan said that the United States is interested in a new arms control architecture involving five nuclear powers with a common missile launch notification regime.
At the same time, the formalization of the notification regime for missile launches by all members of the "five" seems to be a straightforward measure, "based simply on common sense," he added.