Raisi, a hardliner who had been seen as a potential successor to Supreme Leader Ayatollah Ali Khamenei, was killed when his helicopter came down in poor weather in mountains near the Azerbaijan border on Sunday.
"Signs of gunshot or similar were not observed in the wreckage of the helicopter (which) crashed in an area in high altitude and burst into flames," the report issued by the armed forces general staff said on Friday.
"Nothing suspicious has been observed in the control tower's conversations with the flight crew," it added.
More details would be released as the investigation advanced, the report said.
Raisi was buried in the Shi'ite Muslim holy city of Mashhad on Thursday, four days after the crash that also killed foreign minister Hossein Amirabdollahian and six others.
Experts say Iran has a poor air safety record, with repeated crashes, many involving US-built aircraft bought before the 1979 Islamic revolution.
Tehran says US sanctions have long prevented it from buying new aircraft or spare parts from the West to update its creaking fleets.
Iran's top prosecutor this week warned against rumour-mongering on social media amid speculation that the helicopter may have been downed, state media reported.
Security forces have detained a man accused of posting a "false" report which had gone viral on social media with 40 million views, the semi-official Fars news agency reported. The post had cast doubt on the authenticity of state media photos of the helicopter.
Iran proclaimed five days of mourning for Raisi, who enacted Khamenei's policies, cracked down on public dissent and adopted a tough line on foreign policy issues including talks with Washington to revive Iran's 2015 nuclear pact.
A presidential election has been scheduled for June 28.Â
