text: Colonel Steve Warren said more than 20 strikes have been carried out in the past four days, destroying IS positions.
  The raids are in support of Iraqi forces who are trying to retake Falluja from IS.
  Meanwhile there are dire warnings about conditions in the city.
  The IS commander in the city, Maher Al-Bilawi, was killed in bombardments targeting IS fighter positions and gun emplacements, Col Warren said.
  However, the colonel warned that it was unclear how long the battle to retake the city would last.
  Islamic State: The full story
  Some 50,000 civilians remain trapped in the city and have been told via leaflet drops to avoid IS areas and put white sheets on their roofs, Col Warren said.
  The UN says it has reports of people dying of starvation and being killed for refusing to fight for IS.
  "We have dramatic reports of the increase of the number of executions of men and older boys, refusing to fight on behalf of Isil," said Melissa Fleming, a spokeswoman for the UN High Commissioner for Refugees, using an alternative acronym for IS.
  "Other reports say a number of people attempting to depart have been executed, or whipped. One man's leg was amputated reportedly."
  The UN says hundreds of families were able to flee the city on Friday with the help of government forces.
  The assault is being carried out by a combined force comprising thousands of Iraqi army troops, the federal police and Sunni tribal fighters, Col Warren said.
  Militia forces were also involved but had pledged to remain outside the city, he added.
  Falluja fell to IS in 2014, a key moment in its rise that saw it declare a caliphate across swathes of Iraq and Syria.
target: The Islamic State group's commander in the besieged Iraqi city of Falluja is among 70 militants killed in coalition air strikes, the US military says.