The Iraqi air force dropped four million letters over Mosul on Thursday, the US-led coalition said, in a move aimed at providing "empathy and support" for residents of the Islamic State-held city.

The air drop comes after the international Institute for War and Peace Reporting started a campaign called "Letters to Mosul" on October 17, the day Iraqi forces began their operation to recapture Mosul from IS jihadists.

"The letters of empathy and support for Mosul residents were written by Iraqis from all over the country," the coalition said in a statement.

"This initiative by the people of Iraq reassures the residents of Mosul, held hostage by ISIL (IS) for more than two years, that they have not been forgotten and that the rest of Iraq is standing with them, waiting to welcome them back in solidarity when ISIL is defeated."

According to the coalition, the letters are based on 2,160 hand-written notes penned in the days since the Mosul offensive began.

"To our dear people ... we are with you in everything and our hearts to you, and we feel what you feel of cold, hunger, and the harshness of days and you should be patient and endured that victory is close, God willing," one letter states, according to the coalition.

Some 100,000 people have fled Mosul since the Iraqi operation against IS began, and aid organizations have said they fear it could result in the displacement of more than a million people.

The government has encouraged civilians in Mosul -- where a million or more people may still live -- to stay in their homes if possible.

What began as a rapid push into the city has turned into a hellish block-by-block war with IS inflicting high casualty rates on advancing Iraqis.