Nearly 10,000 soldiers, including an Indian Army contingent and China's People's Liberation Army (PLA), took part in the parade on the iconic Red Square here which lasted for over 90 minutes.
The parade on Red Square showcased cutting edge weapons such as the next-generation Armata T-14 tank and advanced military aircraft.
Russian President Vladimir Putin witnessed the parade along with Mukherjee, Chinese President Xi Jinping, and UN Secretary General Ben Ki-moon and several other heads of state.
The term "unipolar" is often used by Russia to criticise the United States' purported aim to dominate world affairs.
"We can see how the force bloc-based thinking has been gaining power. That all is undermining the stable international development," Putin said.
"Our common task should be offering equal-security system for all countries, which is adequate to modern threats, and which is based on regional, global, bloc-free basis," he said.
"We are grateful to the people of Great Britain, France and the United States for their contribution to victory," he said while underlining the importance of global cooperation.
At the parade, military units from across Russia -- some dressed in WW2-era uniforms -- marched, and more than 100 aircraft flew over Red Square.
Also on show was the new, hi-tech Armata battle tank, which has a remote-controlled gun turret and reinforced capsule for the crew, as well as the RS-24 Yars intercontinental ballistic missiles -- each capable of delivering three nuclear warheads.
