He was reacting to comments by Jon Kyl, a Republican senator who said he did not think ratification of the New Start treaty should be considered this year.
Mr Biden said without such approval, the US would be unable to inspect and track the Russian nuclear arsenal.
The treaty aims to reduce the nuclear arsenal of the two countries.
Signed in April by US President Barack Obama and his Russian counterpart Dmitri Medvedev, New Start replaces the Start treaty which expired in December of last year.
"The New Start treaty is a fundamental part of our relationship with Russia, which has been critical to our ability to supply our troops in Afghanistan and to impose and enforce strong sanctions on the Iranian government", Mr Biden said in a statement released by the White House.
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