The vice president also announced the United States will provide an additional $50 million to help Ukraine's beleaguered government with political and economic reforms.
Despite an agreement last week aimed at easing tensions, a weekend shootout at a checkpoint in eastern Ukraine manned by pro-Russia insurgents left at least three dead.
Denis Pushilin, a figurehead of the self-appointed Donetsk People's Republic, says the insurgents do not recognize the Ukrainian government as legitimate.
The Office of the United Nations High Commissioner for Human Rights also reports that in Crimea, it found credible allegations of harassment, arbitrary arrests and torture targeting those who did not support the March 16 secession referendum.
On a voice vote, the Senate approved its version of the legislation. The House endorsed a different version on a 399-19 vote and is poised to pass the Senate version on Friday, the final step needed to send the bill to Obama.
Tensions between Moscow and Kiev have been rising ever since Russian forces occupied the Crimean peninsula and stayed there throughout the referendum last week where votes overwhelmingly supported Russia's annexation.