The Journal cited government and industry officials who were briefed on the mission and said the satellite didn't separate and plunged back into the atmosphere.
These reports are partially based upon a briefing supposedly given to lawmakers and congressional staffers indicating that the satellite did not separate from the rocket as planned.
SpaceX has pushed back its scheduled test fire of the Falcon Heavy rocket by one day.
As for Northrop Grumman, the manufacturer of the Zuma satellite, it simply added "we can not comment on classified missions".
The Falcon 9 rocket was able to make a successful powered landing back on the ground after separating from the upper stage.
Senator Bill Nelson (D-FL), who previous flew into space in the 1980s aboard Columbia as a payload specialist, sided with SpaceX, stating, "The first statement by SpaceX was that the failure to achieve orbit was not theirs".
The secret satellite, called Zuma, was built for the USA government, although it is unclear which part of it. The company chose SpaceX as the launch provider, noting late previous year that it took "great care to ensure the most affordable and lowest risk scenario for Zuma". Questions remained about which national security agency the satellite would have served, as well as its fate. That broke up a longtime and lucrative monopoly held by a joint venture between Lockheed Martin Corp. and Boeing Co. known as United Launch Alliance, which has had 100 percent mission success in its 123 launches.
Zuma mission launch on January 7 in Cape Canaveral, Florida. The company has said it plans about 30 missions in 2018 after completing a record 18 past year.
"I think the rocket itself is considered an extremely reliable vehicle", he said.
Iridium is one of SpaceX's largest commercial satellite customers, with four launches in the past 12 months from Vandenberg Air Force Base on California's central coast and four upcoming launches listed on SpaceX's manifest.
SpaceX said Tuesday that the rocket worked fine, but its statement left open the possibility that something could have gone wrong after the launch.
Northrup Grumman, the maker of the payload, has said it was for the USA government and would be delivered to low-Earth orbit, but offered no other details. It could majorly affect the future business prospects of the company SpaceX associated with the defense, explained the defense analyst at the Lexington Institute, Loren Thompson.