Classified intelligence about the damage to Iran’s nuclear program from U.S. strikes was at the center of a political tempest on Wednesday as spy chiefs pushed out new assessments and President Trump continued to defend his assertion that Iran’s key facilities had been “obliterated.”

The C.I.A. director, John Ratcliffe, said the strikes had “severely damaged” Iran’s nuclear program, and the administration suggested that the initial report, by the Defense Intelligence Agency, was based on preliminary assessments and was already outdated.

The damage was also being assessed by other U.S. spy agencies. No information that has become public from those assessments has supported Mr. Trump’s description of the level of destruction from the U.S. attack, though they all confirmed that the damage had been substantial.

The D.I.A. report was based on information from little more than 24 hours after the American attacks on three of Iran’s nuclear sites.

It described the level of damage as ranging from moderate to severe, according to people briefed on or familiar with its contents.

The report said that if the D.I.A.’s assumption that Fordo, the deepest underground of the sites, sustained a moderate level of damage is correct, then the facility would be inoperable and Iran would not try to rebuild its enrichment capabilities there, one of those people said. If the assumption proved incorrect, the report said, Iran could build a quick version of a nuclear weapon in months.