Iran first denied having being responsible for the incident, in which 176 people were killed, but later admitted the jet was taken down amid fears it was a missile.
The incident came amid rising tensions between the US and Iran, after Donald Trump ordered the killing of military leader Qasem Soleimani.
Prior to the jet incident, Iran had conducted retaliatory strikes for Soleimani's death on bases in Iraq occupied by US troops. They were therefore on high alert for a militarised response from US forces.
In a televised speech on Tuesday, President Rouhani added that the "tragic event" would be investigated thoroughly.
"It was an unforgivable error ... one person cannot be solely responsible for the plane crash," he said.
"Iranian armed forces admitting their mistake is a good first step ... We should assure people that it will not happen again," he said, adding that his government was "accountable to Iranian and other nations who lost lives in the plane crash".
A judiciary spokesman confirmed some people had been arrested for their role in the crash.
It comes after Canadian leader Justin Trudeau blamed the showdown between Donald Trump and Iran’s leaders for the deaths of those on the plane.
He said those who died when the aircraft was downed by an Iranian missile could have been “right now home with their families” if it was not for escalating tensions in the region.
Meanwhile, Tehran has been rocked by protests with demonstrators calling Iranian officials "liars" for denying any involvement in the fatal crash.
An Iranian missile defence system brought down the passenger plane after it took off from Tehran airport.
The military said it mistook the plane for a hostile target after launching a ballistic missile attack on two bases housing US troops in Iraq.