Dmitry Kovtun had been due to appear via video link from Moscow for three days from Monday after reversing a previous decision not to do so in March.
But now the inquiry heard that it looks like Kovtun may not testify after all as he has an obligation of confidentiality to the Russian investigation into the 2006 death of the Kremlin critic.
Kovtun and a second Russian, Andrei Lugovoi, are wanted by British police for allegedly poisoning Litvinenko in a London hotel on November 1, 2006 using tea laced with polonium-210, a radioactive isotope.
Lawyer Robin Tam said that "a suggestion has been made" that Kovtun ask the relevant authorities in Russia for a dispensation, to allow him to give evidence.
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The hearing at the High Court in London has now been adjourned until noon (1100 GMT) on Monday to see if this is possible.
In several interviews from December 2006 onwards, D3 gave German police an account of a conversation he allegedly had with Kovtun in Hamburg on October 30, 2006 before Kovtun flew to London.
D3 said Kovtun had called Litvinenko a "traitor" who "does deals with Chechnya", adding: "There's blood on his hands".