According to the Corporation, which says it has seen and confirmed private messages sent via the WhatsApp messaging service, Maulana Habib Ur Rehman said Mumtaz Qadri was a "true Muslim" and that his death was a "source of grief and immense pain".
Mr Rehman is the lead imam of Glasgow Central Mosque, the biggest mosque and religious center generally in Scotland.
Mumtaz Qadri (below) was the bodyguard of the governor of Punjab Province Salman Taseer, but he murdered him in 2011 because he was an outspoken critic of the country's blasphemy laws - which are often used to target Christians and other minorities.
For example, Asia Bibi has been on death row in Pakistan for five years over a claim she insulted the Prophet Muhammad - one she denies.
Salman Taseer's son Shahbaz (below) was also kidnapped in 2011 after his death, and was only found a few a weeks ago in March 2016.
Mumtaz Qadri was sentenced to death for murdering Mr Taseer and was hung earlier this month. Tens of thousand of Pakistanis attended his funeral.
Maulana Habib Ur Rehman said at Mumtaz Qadri's execution: "I cannot hide my pain today. A true Muslim was punished for doing which [sic] the collective will of the nation failed to carry out.
"Just when France was occupied by Nazies [sic], French did all they had to in order to protect their nation.
"They were national heroes. Hanging Mumtaz Qadri has raised serious questions about Pakistan's independence.
"The issue is not of an individual. The issue is of national identity and Islamic spirit."
"... sending Mumtaz bhai [brother] to gallows is a source of grief and immense pain."
In a statement given to the BBC Mr Rehman said: "Mumtaz Qadri's execution is condemned as it is not in accordance with due process nor is it in accordance with Islamic teachings and principles.
"The selective messages disclosed to you by an unauthorised third party have been misconstrued and taken out of context.
"Capital punishment on this particular occasion was inappropriate and any expressions of sympathy or compassion are extended in my capacity as a private individual and not in any professional or public capacity."
Glasgow Central Mosque has not commented on one of its imams messages.
Separately, it condemned the perpetrators of the Brussels terror attacks on Monday and expressed solidarity with the victims on Facebook:
