"Undoubtedly, we will not be able to leave this without a response," deputy foreign minister Sergei Ryabkov told Interfax news agency ahead of a meeting between the Russian and US foreign ministers.
The Senate bill -- dubbed the Ukraine Freedom Support Act -- must still be approved by the White House, which has so far been reluctant to provide direct military assistance to Ukraine for fear of being drawn into a proxy war with Russia.
The eight-month conflict between government forces and pro-Russian separatists has left at least 4,634 dead and 10,243 wounded, while displacing more than 1.1 million people, according to new figures released by the United Nations.
It also threatens fresh sanctions against Russia, whose economy is crumbling under previous rounds of Western sanctions and a collapse in oil prices.
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Kiev lawmakers have hailed the bill as a "historic decision". They have long been pressing the West to provide military support to their beleaguered army, but have so far received only non-lethal equipment.
A State Department official confirmed to AFP that the meeting would be Sunday after Washington had initially said it was set for Monday.
A tentative ceasefire has been in place along the frontline in eastern Ukraine since Tuesday, and fighting has been greatly reduced despite occasional breaches.
The Ukrainian army on Saturday reported 11 attacks on its positions in the past 24 hours but no one was killed or wounded.