Identical texts of the Ukraine Freedom Support Act passed both the Senate and House of Representatives on Thursday, but because of a technical issue it returned to the Senate where it passed by unanimous consent moments before the chamber adjourned late Saturday night.
It is now up to Obama to either sign or veto the measure. The White House said Thursday it was "looking at it."
On Saturday, one day ahead of a meeting between Russian Foreign Minister Sergei Lavrov and US Secretary of State John Kerry, Moscow warned that "undoubtedly, we will not be able to leave this without a response."
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The legislation authorizes -- but does not legally require -- Obama to provide lethal and non-lethal military aid to Ukraine, including anti-tank weapons, ammunition and troop-operated surveillance drones.
Washington backs Ukraine in its conflict with Russia, but Obama has yet to approve the bulk of an arms request by Kiev.
"The hesitant US response to Russia's continued invasion of Ukraine threatens to escalate this conflict even further, warned bill coauthor Senator Bob Corker.
Congressional passage heaps political pressure on Obama.
On Thursday he signalled he was against unilaterally putting the economic squeeze on Moscow, saying it would be "counterproductive" for Washington to "get out ahead of Europe further" on sanctions.
In November, the Pentagon delivered the first of 20 anti-mortar radar systems to Ukraine.
