Russia wants the process of India and Pakistan's membership to the Shanghai Cooperation Organisation (SCO) speeded up, RIA Novosti reported.
He said delaying the decision on the membership of India and Pakistan was "counter-productive".
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, 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 Afghanistan would help achieve these goals.