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Iraq's prime minister has ordered security forces to pursue the perpetrators of attacks on military bases hosting international coalition advisers, a government military spokesman said on Monday.

The announcement came after a recent spike in rocket and drone attacks against Iraq military bases which host U.S. and other international forces.

"Attacks that target Iraqi bases that houses advisers from the international coalition in Iraq are unacceptable. They are here based on the invitation of the government," said a spokesman for Iraqi Prime Minister and commander-in-chief of the armed forces Mohammed al-Sudani.

Three military bases were attacked by Katyusha rockets and drones in less than a week, including Ain al-Asad in western Iraq, a military base near Baghdad's international airport and Harir in the northern Iraqi city of Erbil.

Iraqi security officials say the prime minister has ordered the stepping up "preemptive security measures" to prevent further attacks on the three Iraqi military bases hosting U.S. and other international forces.

Iraqi armed groups aligned with Iran threatened to target U.S. interests with missiles and drones if Washington intervened to support Israel against Hamas in Gaza.

There has been an increase in attacks against U.S. forces in Iraq and Syria since the start of the war between Israel and Hamas in Gaza.

The U.S. State Department said on Sunday U.S. citizens should not travel to Iraq after recent attacks on American troops and personnel in the region.

The United States has 2,500 troops in Iraq, and 900 more in neighbouring Syria, on a mission to advise and assist local forces in combating the Islamic State group, which in 2014 seized swathes of territory in both countries.