Northrop Grumman, which built the satellite, told Dow Jones through a spokesman: "We cannot comment on classified missions."
"For clarity: after review of all data to date, Falcon 9 did everything correctly on Sunday night," Gwynne Shotwell, President and COO of SpaceX, in a statement sent to CNBC. "If we or others find otherwise based on further review, we will report it immediately. Information published that is contrary to this statement is categorically false. Due to the classified nature of the payload, no further comment is possible."
"Since the data reviewed so far indicates that no design, operational or other changes are needed, we do not anticipate any impact on the upcoming launch schedule. Falcon Heavy has been rolled out to launchpad LC-39A for a static fire later this week, to be followed shortly thereafter by its maiden flight. We are also preparing for an F9 launch for SES and the Luxembourg Government from SLC-40 in three weeks."
The Zuma spacecraft was attached to one of SpaceX's Falcon 9 rockets and launched from the Cape Canaveral Air Force Station in Florida. The Falcon 9 successfully landed back to base.
Landing and reusing rockets is the main aim of SpaceX scientists, who argue that it reduces the cost of launches and allows it to perform more missions.
SpaceX did not reveal the purpose of Zuma because it is classified, but the mission marked Elon Musk's company's first in 2018.
—CNBC's Arjun Kharpal contributed to this report.
For more on the apparently lost satellite, see the full report from Dow Jones.