"On behalf of the European Parliament, I call upon both the Russian and Ukrainian authorities to uphold the agreement mediated by the European Union which they also signed," Hans-Gert Pottering said in a statement.
He said Russia and Ukraine must resolve as soon as possible the bilateral gas dispute, which "caught the EU citizens in the crossfire."
"The European Union wants to be assured that both Russia and Ukraine are reliable partners in energy supply," Pottering said.
Under Monday's deal with the European Union and Ukraine, Russia's energy giant Gazprom on Tuesday resumed pumping gas into Ukraine for transit to Europe. However, the transit gas did not reach Europe.
Moscow immediately accused Kiev of stealing gas which was meant for Europe.
In response, Ukrainian energy company Naftogaz warned on Monday that Ukraine would continue using Russian gas being transited to European countries for technical purposes.
However, Gazprom said Ukraine should either use its own "technical" gas, or buy it if the company lacks its own resources.
The move to resume gas supplies to Europe was made after Russia, Ukraine and the EU agreed on the presence of international monitors at Ukrainian and Russian gas transportation facilities to oversee gas transit.
Russia halted gas supplies to Europe on January 7, accusing Ukraine of tapping transit gas, which Ukraine denied.
Moscow cut off gas deliveries to Ukraine on January 1 after the parties failed to agree a settlement on Kiev's debt for supplies in 2008 and a price for a 2009 contract.