WASHINGTON - US President Barack Obama on Monday urged Iraqi's Prime Minister-designate Haider al-Abadi to form an inclusive cabinet "as quickly as possible."

"Earlier today, Vice President (Joe) Biden and I called Dr. Abadi to congratulate him and to urge him to form a new cabinet as quickly as possible -- one that's inclusive of all Iraqis, and one that represents all Iraqis," Obama said from his vacation home in Massachusetts.

"I pledged our support to him," he said, noting that Iraqi President Fuad Masoum's nomination of Abadi as new prime minister "is an important step towards forming a new government that can unite Iraq's different communities."

Obama also called on all Iraqi political leaders to work " peacefully" through the political process in the days ahead.

On Monday, politicians allied to outgoing Iraqi Prime Minister Nuri al-Maliki rejected Abadi, saying he is not representing them and has no legitimacy.

Summing up US military operations in Iraq, Obama said American forces have successfully conducted targeted air strikes to prevent terrorist forces from advancing on the northern city of Erbil and to protect American civilians there over the past few days.

"We've stepped up military advice and assistance to Iraqi and Kurdish forces as they wage the fight against ISIL," Obama said, referring to the Islamic State of Iraq and the Levant.

The United States has begun shipping weapons to the Kurdish forces battling ISIL, State Department spokeswoman Marie Harf told reporters on Monday.