The Islamic State (IS) terrorist group has established unlawful sharia courts in areas under its control and is carrying out "cruel and inhuman" punishments against men, women and children, the United Nations human rights agency says.

The Office of the High Commissioner for Human Rights (OHCHR) said those who faced punishments had been accused of violating the group's extremist interpretations of Islamic law.

"The ruthless murder of two men, who were thrown off the top of a building after having been accused of homosexual acts by a so-called court in Mosul, is another terrible example of the kind of monstrous disregard for human life that characterised ISIL's reign of terror over areas of Iraq that were under the group's control," OHCHR spokeswoman Ravina Shamdasani said.

The United Nations said an IS website also posted photos of two men being crucified after they were accused of banditry.

The men were hung up by their arms and then shot dead.

Photos were also posted of a woman being stoned to death, allegedly for adultery.

Four doctors were recently killed in central Mosul, allegedly after refusing to treat IS fighters, the UN said.

Educated women being executed: reports

The OHCHR also received numerous other reports of women who had been executed by IS in Mosul, Iraq, and other areas under the group's control, often immediately following sentences passed by its sharia courts.

"Educated, professional women, particularly women who had run as candidates in elections for public office, seem to be particularly at risk," Ms Shamdasani said.

"In just the first two weeks of the year, reports indicated that three female lawyers were executed."

She said the group also reportedly executed 15 civilians in front of a large crowd in Fallujah in January on suspicion they had cooperated with Iraqi security forces, and 14 more in a public square in Dour, north of Tikrit, for refusing to pledge allegiance to IS.

Ms Shamdasani said the OHCHR would continue to document human rights abuses and violations taking place in Iraq.

It is expected to present a report to the Human Rights Council in March.