Republicans joined with the majority of Democrats to easily send the bill toward a final vote, 78 to 17.
Foreign Relations Committee Chair Bob Menendez, D-N.J., Armed Services Committee ranking member John McCain, R-Ariz., and Majority Whip Dick Durbin, D-Ill., warned a failure to pass the legislation would only encourage Putin to further push his country's borders outward.
Seventeen senators, all Republicans, voted against the measure, including Sens. Rand Paul of Kentucky and Ted Cruz of Texas.
The Senate version of the legislation would send $150 million in assistance, along with a $1 billion loan guarantee. The House passed similar legislation, but Republicans in the lower chamber will likely block the Senate version over disagreements on International Monetary Fund reforms.