The mysterious explosion of a SpaceX rocket last month took an odd turn with a "cordial" encounter between staff of Elon Musk's firm and fierce rival United Launch Alliance, The Washington Post reported.

No one was hurt in the September 1 blast, which came as the unmanned Falcon 9 rocket was being fueled ahead of a standard, pre-launch test in Cape Canaveral, Florida.

Musk is rushing to revolutionize the launch industry by making rocket components reusable.

And the accident -- the second of its kind since SpaceX was founded in 2002 -- came just over a year after a Falcon 9 rocket failed after liftoff on June 28, 2015, destroying a Dragon cargo capsule bound for the International Space Station (ISS).

Before that, SpaceX had logged 18 successful launches of the Falcon 9 -- including six of 12 planned supply missions to the ISS carried out as part of a $1.6 billion contract with NASA.

During their investigation SpaceX officials found something suspicious they wanted to check out, the Post said, quoting three industry officials with knowledge of the episode.

SpaceX had still images from video that seemed to show a shadow, then a white spot on the roof of a nearby building belonging to ULA, the Post said.

ULA is a joint venture between Lockheed Martin and Boeing.

So a SpaceX employee visited ULA facilities at Cape Canaveral, Florida and asked for access to the roof at one ULA building that had a close line of sight to the SpaceX launch.

The visit was cordial, not accusatory. The ULA people denied access, but notified the Air Force, which inspected the roof and found nothing connected to the blast, the Post said.