The statement on Saturday morning blames "human error" for the incident.
Press TV also quoted Iran's General Staff of the Armed Forces as saying that the plane had flown close to a "sensitive military site".
In a statement posted on social media, Iranian President Hassan Rouhani wrote that the country "deeply regrets this disastrous mistake."
"My thoughts and prayers go to all the mourning families. I offer my sincerest condolences," he said, adding that "investigations continue to identify and prosecute this great tragedy and unforgivable mistake."
Al Jazeera's Assed Baig, reporting from Tehran, said that authorities acknowledged that the country's air defence system "mistakenly" shot the plane down.
Iran had denied for several days that a missile downed the aircraft. But then the US and Canada, citing intelligence, said they believe Iran shot down the aircraft.
On Friday, Ali Abedzadeh, head of Iran's civil aviation department, said it was impossible due to close coordination between Iran's air defence and civil aviation department.
"What is obvious for us, and what we can say with certainty, is that no missile hit the plane,"
The jetliner, a Boeing 737 operated by Ukrainian International Airlines, went down on the outskirts of Tehran during takeoff just hours after Iran launched a barrage of missiles at US forces in Iraq.
Al Jazeera's Baig said that questions are now raised why Iranian authorities kept the country's air space open during a military operation.
In a social media post, Iranian Foreign Minister Javad Zarif said that "human error at time of crisis caused by US adverturism led to the disaster."
"Our profound regrets, apologies and condolences to our people, to the families of all victims, and to other affected nations."
The plane, en route to the Ukrainian capital of Kyiv, was carrying 167 passengers and nine crew members from several countries, including 82 Iranians, 57 Canadians and 11 Ukrainians, according to officials.
SOURCE: Al Jazeera and news agencies
Tags
Society