"We ask our partners not to lift sanctions until Ukraine takes control of its entire territory," Yatsenyuk said.
He spoke just hours after US President Barack Obama offered to lift sanctions against Moscow if it threw its weight behind an unraveling peace deal with Kiev.
Yatsenyuk said Russia must abide by "all points" of a peace deal that provides for autonomy in eastern Ukraine, where pro-Moscow rebels have been fighting Kiev since April.
"Every day, despite the ceasefire, we are losing Ukrainian soldiers, we are losing civilians and the shelling is still going on," he said.
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He called on Moscow to withdraw its troops from Ukraine and cut off support to the rebels in eastern Ukraine. Russia has repeatedly denied that it is providing aid to the insurgents.
"We are the country that needs peace, and it's difficult to hammer out any kind of peace deal, starring down the barrel of a gun," he said.
In his address to the 193-member assembly, Obama earlier said that the recent ceasefire deal in eastern Ukraine offered an opening towards diplomacy and peace.