Mosul is the largest urban center under the militants' control, and had a pre-war population of nearly 2 million.
Its fall would mark the effective defeat of Islamic State in Iraq, according to Prime Minister Haider al-Abadi, who has said he aims to retake the city this year.
The Iraqi army is trying to close in from the south. In July it captured the Qayyara airfield, 60 km (35 miles) south of Mosul, which is to serve as the main staging post for the anticipated offensive.
The Peshmerga operation on Sunday was "one of many shaping operations that will also increase pressure on ISIL in and around Mosul," said an official from the Kurdistan Regional Security Council, using another acronym to refer to IS.
"Noose tightening around #ISIL terrorists: #Peshmerga advancing east of #Mosul, #ISF shoring up south near #Qayyara,"tweeted Brett McGurk, the U.S. envoy to the coalition fighting the militant group.
Preparations for the offensive on Mosul are "approaching the final phase," McGurk told reporters during a visit to Baghdad on Thursday. He said the planning included considerations for humanitarian aid to uprooted civilians.