The call was given by Russia's acting Foreign Minister Sergei Lavrov while participating in a meeting of foreign ministers of the SCO member states in Beijing Friday.
He also said delaying the decision on their membership was "counterproductive".
The SCO, set up in 2001, includes Russia, China, Uzbekistan, Kazakhstan, Tajikistan and Kyrgyzstan.
Pakistan, India, Iran and Mongolia have observer status while Turkmenistan and Afghanistan attend SCO gatherings as guest nations.
China has held the organisation's rotating presidency since Aug 1, 2011.
Meanwhile, during the meeting, Lavrov said that an international meet on Afghanistan will take place in Kabul June 14.
"We should actively participate in all international discussions on Afghanistan-related problems, coordinating our positions and stressing the SCO's readiness to constructively contribute to efforts by the international community aimed at the political and economic revival of Afghanistan," said Lavrov.
The minister said granting SCO observer status to the country (Afghanistan) would help achieve these goals.
Russia has no common border with Afghanistan, but the two countries are only separated by former Soviet Central Asian republics that have porous borders with Russia and Afghanistan.