Obama laid out his vision of a nuclear-free world in a speech in Prague last April.
But citing unnamed officials, the newspaper said the Obama administration is now locked in internal debate over a top-secret policy blueprint for shrinking the US nuclear arsenal and reducing the role of such weapons in country's military strategy.
Officials in the Pentagon and elsewhere have pushed back against proposals to cut the number of weapons and narrow their mission, the report said.
In turn, White House officials, unhappy with early Pentagon-led drafts of the blueprint known as the Nuclear Posture Review, have stepped up their involvement in the deliberations and ordered that the document reflect Obama's preference for sweeping change, The Times noted.
The Pentagon has stressed the importance of continued US deterrence, an objective Obama has said he agrees with, the report said.
But a senior defense official, who described the debate as "spirited," acknowledged that some officials are concerned that the administration may be going too far, the paper pointed out.