BAGHDAD — Under pressure from American officials here, Iraq has withdrawn Shiite militiamen from the Ramadi area in Anbar Province, and the American-led coalition immediately responded by stepping up bombing raids to support Iraqi forces battling extremists of the Islamic State there, according to Iraqi officials involved in the decision.

The American ambassador, Stuart E. Jones, met Saturday with Anbar tribal leaders and provincial officials and expressed his dissatisfaction that Shiite militiamen were in the thick of a local offensive against the Islamic State near the Anbar provincial capital, according to two participants in the meeting, interviewed Sunday.

He warned that unless the militias were withdrawn, the United States would not be able to launch airstrikes to support the Iraqi forces there. Anbar Province is a Sunni area, and the tribes who live there have largely opposed the use of Shiite militias in the area, a position the United States supports. American officials worry that the use of Shiite militias will drive more of Anbar’s Sunnis into supporting ISIS, as the Islamic State is also known, and are also concerned about the possibility of accidentally bombing the undisciplined and disorganized militia forces.

“The American ambassador told us that the Americans will not carry out airstrikes if the popular mobilization stays in Anbar, and we understood him,” said Sabah Karhot, head of the Anbar Provincial Council, one of those at the meeting.