For days after the Jan. 8 shootdown, Iran denied that it fired missiles at the plane.
Hassan Rezaeifar was quoted by the state-run IRNA news agency as saying "we have no plans to send them out.”
Iran does not have the equipment necessary to be able to analyze the damaged black boxes quickly.
The aid in question was held up last summer on orders from Trump but was released in September.
Iran's Judiciary spokesman Gholamhossein Esmaili said “some individuals" were arrested after “extensive investigations."
A candlelight ceremony in Tehran turned into a protest, with hundreds of people chanting against the country's leaders.
Newspapers called for resignations and sackings over the handling of the air disaster.
Zelensky requested that 45 Ukrainian experts already on the site have full access through the course of the investigation.
Western leaders said the plane appeared to have been unintentionally hit by a surface-to-air missile near Tehran.
The Iranian report suggests a sudden emergency struck the Boeing 737 operated by Ukrainian International Airlines.