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.
The crash came hours after Iran launched a ballistic missile attack on Iraqi bases housing U.S. soldiers.
NATO's commander declined to say whether the missiles had made it to Ukraine's front lines yet.
An official says the Army and local law enforcement are providing security as he testifies during the impeachment hearing.
House Democrats released Anderson's testimony as part of a new public phase of the ongoing impeachment inquiry.
The Pentagon has long watched the war in Ukraine as a blueprint for where it could apply its own lessons.