The laws additionally allow the two companies' forces greater access to weapons than private security firms and more freedom to use these arms.
Gazprom currently has around 430,000 employees and controls many of Russia's leading media outlets. It also owns the country's third largest bank and has a virtual monopoly on gas exports - while all the time enjoying close links with the Kremlin.
"This law is like a Pandora's Box," Gennady Gudkov, a lawmaker with the left-wing Fair Russia party, which opposed the law, is quoted by the Reuters news agency as saying.
"Gazprom and Transneft are proposing the creation of their own corporate armies," he told the chamber.
"If we pass this law we will all become the servants of Gazprom and Transneft. These companies seem to be following the maxim ... that what is good for them is good for Russia."
Gazprom has recently said that it is looking at gaining a foothold in the UK market and has been linked with a possible takeover of Centrica.
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