DAVOS, Switzerland — Prime Minister Haider al-Abadi of Iraq privately asked Defense Secretary Ashton B. Carter this week for additional help training Iraqi police forces used to secure cities that have been retaken from the Islamic State, senior Defense Department officials said.

The request opens the door for the United States and other countries — particularly Italy, which has expertise in police training — to become more involved in assisting the Iraqis.

Mr. Abadi told Mr. Carter that even the minimal training the police forces had received significantly enhanced their ability to maintain control of the city of Ramadi, which the Iraqi government reclaimed last month, the officials said.

The newly trained police forces have held the city well enough that some of Iraq’s most capable military forces, which captured the city, have been able to leave Ramadi sooner than expected and take on new missions, said one of the Defense Department officials, who spoke on condition of anonymity to describe the conversation on bilateral security.