A statement issued by Ban's press office said he was dismayed by the post-election violence, "particularly the use of force against civilians."
Demonstrators have been gathering almost daily in Tehran since authorities said incumbent President Mahmoud Ahmadinejad had easily defeated challenger Mirhossein Mousavi in the June 12 vote.
Iranian television said 10 people were killed on Saturday and the hardline Revolutionary Guards vowed on Monday to crush resistance by "rioters."
The U.N. statement said Ban "calls on the authorities to respect fundamental civil and political rights, especially the freedom of expression, freedom of assembly and freedom of information."
"He urges an immediate stop to the arrests, threats and use of force," it added.
The statement also said Ban called on the Iranian government and the opposition to resolve their differences peacefully through dialogue and legal means.
The bulk of the statement made clear that Ban, whose only previous statement on the crisis called for the will of the Iranian people to be fully respected, was directing his main criticism at the authorities. (Reporting by Patrick Worsnip; Editing by Alan Elsner)
