BAGHDAD, June 13 -- Several of Iraq's most powerful Iran-aligned armed factions have pledged to place their weapons under state control, a shift the government is hailing as a milestone but one that is unfolding under intense American financial pressure and that the strongest militias are already refusing to accept.

The pledges have accumulated over recent weeks. Asaib Ahl al-Haq, a group Washington lists as a foreign terrorist organisation, said it would hand its arms to the state, and Saraya al-Salam, the force loyal to the cleric Muqtada al-Sadr, marked its separation from his political movement at a ceremony in Samarra, its fighters folding into the official security forces.

The push is led by Prime Minister Ali al-Zaidi, who took o...