Coroner Robert Owen, who is overseeing an inquest, had asked the government to hold a broad inquiry into the death of the KGB agent turned Kremlin critic, who died in London in 2006 after drinking tea laced with radioactive polonium-210.
In Britain, coroners typically hold inquests in public to determine the facts about violent or unexpected deaths.
Lawyers for Litvinenko's family say he was working for Britain's intelligence services when he died, and that the Kremlin ordered his killing.
Owen said that unlike a coroner's inquest, an inquiry would be able to consider secret evidence to determine whether the Russian state was involved.
Last week Owen said the government had refused his request. In a letter published today, Home Secretary Theresa May spelled out her reasons, among them the financial cost. She also said "it is true that international relations have been a factor in the government's decision-making."
"An inquest managed and run by an independent coroner is more readily explainable to some of our foreign partners, and the integrity of the process more readily grasped, than an inquiry, established by the government, under a chairman appointed by the Government, which has the power to see government material potentially relevant to their interests, in secret," May wrote.
Litvinenko's widow Marina has accused Britain of putting relations with Russia ahead of uncovering the truth.
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