No third party should intervene in U.S. whistleblower Edward Snowden's attempts to secure political asylum, according to Russian politicians and officials.

"An agreement of the side ready to deal with him is needed ... Snowden expects to sort out all the issues regarding his further residence with the countries to which he has applied for political asylum," Alexei Pushkov, head of the international affairs committee in the Russian lower house of parliament, told the Interfax news agency Wednesday.

Earlier, Mikhail Fedotov, head of the Russian Presidential Human Rights Council, suggested the UN Refugee Commissioner take a hand in the fate of the former National Security Agency contractor, who has been stuck in Moscow's airport transit area since June 23.

"It will be the best outcome if the UN High Commissioner for Refugees (Antonio Guterres) intervenes," Fedotov told Interfax, adding it was necessary to act within the relevant international conventions.

Meanwhile, Pushkov said there was no indication the fugitive whistleblower had asked the UN commissioner to intervene.

"So the issue will be solved between him and a country which will grant him asylum," Pushkov said.

A similar position was voiced by Valentina Matviyenko, head of Russia's Federal Council, or upper house of the parliament.

"Snowden didn't ask Russia (to grant him asylum). So there could not be any action from our side," Matviyenko told reporters, describing the situation as "grave and deadlocked."

"What can Russia do? He is in a transit area legally as a transit traveller," Matviyenko said.

On Tuesday, Venezuelan authorities said Caracas would contact the Russian government on security measures and provide humanitarian asylum to Snowden in accordance with international law regardless of an extradition demand from the United States.