May's letter to Robert Owen, a senior judge named as the coroner investigating the death of Alexander Litvinenko, did not name Russia, The New York Times reported. May talked about "some of our foreign partners."
"It is true that international relations have been a factor in the government's decision making," she said.
Litvinenko, 43, had recently become a British citizen when he died in 2006. He was poisoned with polonium 210, a highly toxic isotope of polonium.
Russia has refused to extradite Andrei K. Lugovoi, another former KGB agent charged in Britain with killing Litvinenko.
In her letter, May said an inquest would be suitable for meeting the government's goal of keeping the investigation as public as possible and involving Litvinenko's widow, Marina, and other members of his family.
"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, which has the power to see government material potentially relevant to their interests, in secret," May said.