as human shields, the UN says.
The group also killed some 190 former members of Iraq's security services and 42 civilians, apparently for refusing to obey its orders, the UN adds.
Iraqi, Kurdish and allied forces have advanced on their push to retake Mosul, IS's de facto capital in Iraq.
As many as 1.5 million people are believed to remain there.
There are fears IS could use them to defend itself as the operation gets closer to the centre of the city.
"Credible reports" suggested that civilians in sub-districts around Mosul had been forced from their homes and relocated inside the city since the offensive began earlier this month, UN spokeswoman Ravina Shamdasani said.
Media captionBattle for Mosul: Inside the Kurdish advance on the last IS stronghold Media captionResidents of Mosul tell an Iraqi radio station of the fear of living in the city held by the IS group
Men, women and children from 6,000 families were abducted in areas including Shura, she added.
"Isil's depraved cowardly strategy is to attempt to use the presence of civilian hostages to render certain points, areas or military forces immune from military operations, effectively using tens of thousands of women, men and children as human shields," Ms Shamdasani added, using an acronym for IS.
She said the allegations had been corroborated by the UN but added that the true number might be greater.
The UN said last week so-called Islamic State was apparently not allowing families to flee for territory held by the Iraqi army outside Mosul and that civilians suspected of being disloyal to the group appeared to had been targeted.
The organisation added that only "modest" numbers of people had so far fled Mosul.