Mr Peskov claimed that Ukraine has not responded to a draft document that includes a proposal to set up three working groups.
Mr Rubio told NBC, ““We are the only ones that can talk to Ukraine and Russia, and everyone has encouraged us to play that role.”
Mr Zelensky also criticised China for hosting Mr Putin during his recent four-day state visit.
Current rules permit Russians with diplomatic or official documentation to travel to China.
Europe braces for the outcome of President Donald Trump’s face-to-face discussions with his Russian counterpart, Vladimir Putin, later this week.
Messrs Putin and Zelensky have not met since December 2019.
Switzerland points out that as the host of international conferences, it must grant exemptions for entry on such occasions.
Mr Simonenko faces up to 10 years in a penal colony.
Mr Trump appears to be frustrated with Mr Putin’s determination to continue the war in Ukraine despite overtures from the American leader seeking a ceasefire and peace deal.
Mr Araghchi arrived in Moscow on Sunday to hold talks with the Russian leadership.
