Prime Minister-designate Haider al-Abadi asked Iraqis on Tuesday for unity in the fight against the jihadists, while controversial incumbent Premier Nuri al-Maliki still refused to say whether he is willing to step down to put an end to the political crisis.

Al-Abadi, named on Monday to form a new government, said that defeating terrorism is his chief priority because it directly threatens the country, though he noted that Iraq now faces "many challenges to its unity, its social fabric and all its components."

He called on all political movements to "believe in the constitution and in the democratic political process," to join forces in response to the challenges, and to "keep and open mind and sit down together, not to form a government, but to develop a national determination to deal with our problems."

He also asked for the cooperation of allied nations and international organizations to fight the jihadist Islamic State.

Al-Abadi, whose nomination was welcomed by the U.S. and Iranian governments, received congratulations Tuesday from Saudi Arabia's King Abdullah.

President Fouad Massoum, a Kurd, turned to al-Abadi a day after al-Maliki said he was suing the head of state for failing to nominate him for a third term as prime minister.

Al-Maliki's Dawa party got the largest number of seats in April's legislative elections, but the broader Shiite coalition of which it is a part, the Iraqi National Alliance, has soured on the premier, whose rule has alienated many Sunnis and Kurds.

Al-Abadi, himself a member of Dawa, extended an olive branch to al-Maliki on Tuesday, praising his efforts to combat terrorism and build the Iraqi state, and assuring him he will continue to be a "brother, comrade and key partner" in the political process.

Al-Maliki on Tuesday urged the army and police to stay out of the political crisis and limit themselves to their duties of maintaining security and protecting the country.

Meanwhile the clashes among jihadists, Iraqi forces and Kurdish troops continue and on Tuesday at least 80 IS combatants were killed in airstrikes.

The airstrikes were aimed at "important" IS positions near the northern city of Mosul, the security chief of Nineveh province, Mohammed al-Bayati, told Efe.

The deadliest bombing occurred in the city of Sinjar, recently overrun by the IS.

At the same time, at least two people died, including a pilot, and another 20 were injured when a helicopter crashed that was transporting humanitarian aid to members of the Yazidi religious minority who fled to Mt. Sinjar after IS seized the city.

U.S. forces also carried out further airstrikes aimed at preventing an IS assault on Irbil, capital of the Kurdish autonomous region.

U.S. Vice President Joe Biden telephoned Kurdistan Regional President Masoud Barzani on Tuesday to urge him to cooperate with al-Abadi to form a government "representative of all Iraqis," the White House said.

Barzani expressed "his willingness to work with Abadi and other leaders to bring Iraq's different communities together to confront the nation's political, economic, and security challenges," according to the White House statement.