India had been seeking the extradition of Rana, a Canadian national of Pakistani origin, who is wanted for the 2008 Mumbai terrorist attacks case.
Rana approached the US Supreme Court last month against his extradition to India after he lost the legal battle in lower courts.
It was the last call from Rana to the US Court of Appeals for the North Circuit in San Francisco where, after losing all the lower courts and many federal courts, the legal battle had reached its last stage.
Rana's last legal hope not to be extradited to India had arrived.
On December 16, US Solicitor General Elizabeth B Prelogar urged the Supreme to reject the petition. Rana's counsel Joshua L Dratel, in his response on December 23 challenged the US Government's recommendation and pleaded with the Supreme Court that his writ be accepted.
He is accused of having been involved in the 26/11 Mumbai attacks and has a close connection with Pakistani-American Lashkar-e-Taiba (LeT) terrorist David Coleman Headley, one of the prime conspirators behind the terror strike that targeted India's financial nerve centre in 2008.
The total death toll from the Mumbai terror attacks that were laid down by 10 Pakistani terrorists over a more than 60-hour siege attacking and killing people at iconic and vital locations in Mumbai is 166 people, including six Americans.
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