"After it [the appeal] arrives via diplomatic channels, it will be reported and considered by the Russian president", Peskov told reporters.
He did not comment on media reports that Russia and Israel were discussing at the highest level the possibility of exchanging Issachar for Alexei Burkov, who is suspected of "hacking" and is going to be extradited to the United States.
"I will not comment on it, this refers to the content of bilateral contacts, which we do not publish, unlike other countries", Peskov said.
Rivlin wrote on Twitter that on Sunday he had asked Putin to pardon the Israeli woman Naama Issachar, who had been sentenced on Friday to 7.5 years in prison for smuggling and possession of drugs.
Issachar was detained on 9 April in Sheremetyevo airport en route from New Delhi to Tel Aviv with some 9 grams (0.32 ounces) of drugs. She pleaded guilty to drug possession but denied her guilt of smuggling.
The office of Israeli Prime Minister Benjamin Netanyahu said that he had discussed the Issachar case with Putin, in particular, asked to mitigate both the punishment and the conditions of detention. Israeli newspaper Haaretz said, citing sources, that the Russian side had raised the issue of exchanging Issachar for Burkov. The newspaper claimed that this issue had been mentioned during a meeting between Netanyahu and Putin in Sochi.
Burkov was detained by Israeli police in the Ben Gurion international airport in 2015 on an arrest warrant issued by US authorities, presumably for hacking activities. His extradition was considered in a Jerusalem district court behind closed doors.