Washington also came down hard on the move to convene a meeting of the Permanent Council of the Organisation of American States to consider the Assange issue.
A State Department statement said, "The United States is not a party to the 1954 OAS Convention on Diplomatic Asylum and does not recognise the concept of diplomatic asylum as a matter of international law."
The US statement came as the WikiLeaks founder continued to hole up in the Ecuador Embassy in Britain, with no signs yet of his move to seek a passage to Quito.
As the stalemate between Britain and Ecuador continued on the issue, Quito has offered to let Assange stay indefinitely in its embassy in London. Ecuador has also turned to OAS to seek support for its move to offer asylum to the fugitive Australian.
"We believe this is a bilateral issue between Ecuador and the United Kingdom and that the OAS has no role to play in this matter," the State Department said.
Supporters of the WikiLeaks founder believe that Assange is at risk of extradition to the US after angering American authorities by leaking out sensitive diplomatic cables.
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Ecuador yesterday granted political asylum to WikiLeaks founder Julian Assange, setting stage for an unprecedented diplomatic stand-off with the UK, which has threatened to extradite him to Sweden come what may.
Assange dramatically sought refuge in the Ecuadoran embassy in London to evade extradition to Sweden to face sexual assault charges.