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 Friday, 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.
"However this has not been a decisive factor and it if had stood alone would not have led the government to refuse an inquiry."
Litvinenko's widow Marina has accused Britain of putting relations with Russia ahead of uncovering the truth.