The 60-year-old kingpin, accused of running the Sinaloa cartel -- one of the world's biggest drug empires -- was extradited to New York on January 19, and is being held in solitary confinement in Manhattan pending trial next April.
But in a new court filing, his public defender lawyers say his extradition violated the terms of Mexico's initial agreement to send Guzman to either Texas or California, and violated the Mexico-US extradition treaty.
"These conditions... Are tantamount to torture. Had Mexico been advised of these conditions, it almost certainly would not have consented to Mr Guzman's detention and prosecution in this district," said the court papers.
His lawyers are also challenging the US government's desire to seize USD 14 billion in Guzman's purported drug profits, saying there was "no evidence" the United States sought permission from Mexico to pursue such a forfeiture.
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Federal Judge Brian Cogan has yet to rule on the request.
The defense repeatedly has challenged the conditions of his custody.
In May, Cogan agreed to relax only slightly just a handful of the conditions, allowing him to exchange pre- screened written messages with his wife but denying him family visits and phone calls.