An array of Iran-backed Iraqi militia groups have agreed to suspend rocket attacks on U.S. forces on the condition that Iraq's government presents a timetable for a withdrawal of American troops, one of the groups said on Sunday.

"The factions have presented a conditional cease-fire," said Mohammed Mohi, spokesperson for the Iran-backed Kataib Hezbollah group. "It includes all factions of the (anti-U.S.) resistance, including those who have been targeting U.S. forces," he told Reuters.

Mohi said the Iraqi government must implement a parliamentary resolution in January that called for the withdrawal from Iraq of foreign troops.

The parliament's decision came after a U.S. drone strike at Baghdad airport killed Iranian military mastermind Qassem Soleimani and Iraq's top Shiite paramilitary chief Abu Mahdi al-Muhandis, raising fears of a full-scale Iran-U.S. confrontation on Iraqi soil.

Mohi said there was no deadline for the government to implement the decision, but warned: "If America insists on staying and doesn't respect the parliament's decision then the factions will use all the weapons at their disposal."

He said the firing of Katyusha rockets at U.S. forces and diplomatic compounds had been merely "a message that you're not welcome in the country" and that worse attacks could follow.

U.S. officials blame Kataib Hezbollah for dozens of rocket attacks against U.S. installations in Iraq.

Kataib Hezbollah denies carrying them out. Smaller and previously unknown militias have claimed some of the attacks. Iraqi security sources believe those groups are linked to Kataib Hezbollah and other larger Iran-aligned militias.