BAGHDAD, Iraq (CNN) -- Faced with walkouts by members of his government and increasing criticism from U.S. officials, Iraqi Prime Minister Nuri al-Maliki told U.S. senators Sunday to butt out of his country's domestic politics.
Iraqi Prime Minister Nuri al-Maliki, shown August 16, accused U.S. lawmakers of "severe interference."
"There are American officials who consider Iraq as if it were one of their villages, for example Hillary Clinton and Carl Levin," al-Maliki told reporters in Baghdad. "This is severe interference in our domestic affairs."
Clinton, the early Democratic front-runner in the 2008 presidential contest, and Levin, the chairman of the Senate Armed Services Committee, said last week that Iraq's parliament should replace al-Maliki when it reconvenes next month.
They said his year-old government has not taken the political steps necessary to end the fighting that has ravaged Iraq since the 2003 U.S.-led invasion.
"Carl Levin and Hillary Clinton are from the Democratic Party and they must demonstrate democracy," al-Maliki said. "I ask them to come to their senses and to talk in a respectful way about Iraq."
Al-Maliki said French Foreign Minister Bernard Kouchner, during a visit last week to Baghdad, also asked for his government's removal.
The prime minister said he has demanded an apology from the French government
President Bush said last week that he continues to support the prime minister.
But he acknowledged "a certain level of frustration" with the Iraqi government, whose efforts are backed by more than 160,000 U.S. troops.
Al-Maliki has also come under heavy criticism from Bush's Republican allies, who have so far blocked congressional Democratic efforts to bring American troops home.
Sen. John Warner, a senior Republican and influential former chairman of the Senate Armed Services Committee, just returned from Baghdad with Levin.
Last week, Warner urged Bush to start the process of bringing U.S. troops home from Iraq in September. Watch Warner's proposal pick up a supporter »
On Sunday, Warner said he may support Democratic legislation ordering withdrawals if Bush does not set a timetable.
"I don't say that as a threat, but I say that is an option we all have to consider," he told NBC's "Meet the Press" on Sunday.
Meanwhile, former interim Prime Minister Ayad Allawi has enlisted the aid of a powerful GOP lobbying firm in Washington in an effort to replace al-Maliki's government.
U.S. officials have been pressing Iraqi leaders to pass a package of measures aimed at settling the four-year-old war, in which some 3,700 Americans have died.
Estimates of Iraqi deaths range from 70,000 to hundreds of thousands.
Government leaders said Sunday they had reached agreement on some of those measures. But the top Sunni Arab in the Iraqi leadership, Vice President Tariq al-Hashimi, played down the reports of progress, and his office called the agreements "not so significant."
The benchmarks Congress has set to to judge the Iraqi government's progress include passage of legislation allocating Iraq's oil revenues, easing restrictions on former members of executed dictator Saddam Hussein's Baath Party and setting up provincial elections.
Al-Maliki spokesman Ali al-Dabbagh said Sunday that Iraq's three-member Presidency Council, along with the prime minister and Kurdish regional leader Massoud Barzani, have agreed to push for provincial elections and easing de-Baathification when parliament reconvenes September 1.
"Being a member of the Baath party is not a crime," al-Dabbagh said. "It depends on what the individual did to others."
The leaders also agreed to speed the processing of prisoners held without charges.
But al-Hashimi's office said Sunday's deal sends the proposed laws to a "preparatory committee" for further discussion. The Iraqi Accord Front, a Sunni alliance that quit al-Maliki's government August 1, said it has no plan to return to the government.
Al-Hashimi's party is a member of the front, but he has remained in the government. But al-Dabbagh said Sunday's agreements "reduced part of the conflict that was there, will open dialogue, and will probably make trust be more between the parties."
And the White House, which is required to report to Congress on the progress of the war by mid-September, hailed the deal as a sign the Iraqi leaders are committed to working together.
"We will continue to support these brave leaders and all the Iraqi people in their efforts to overcome the forces of terror who seek to overwhelm Iraq's democracy," White House spokeswoman Emily Lawrimore said.
Those disruptive forces were evident in Sunday's violence. Militants opened fire on unarmed Shiite pilgrims traveling south of Baghdad on a religious trek to Karbala, killing one woman and wounding six other people -- including women and children, an Iraqi Interior Ministry official told CNN.
The incident started around 10:30 a.m. (2:30 a.m. ET) south of Baghdad in Saidiya, an area once populated with Sunnis and Shiites but now predominantly inhabited by Sunnis.
Militants fired small arms weapons at the pedestrians. Shiite militiamen who escorted the pilgrims returned fire, security sources said. There was no immediate word on whether any militants suffered casualties.
Baghdad authorities have banned motorcycles, bicycles and carts from the streets in an effort to protect the pilgrims.
The faithful are headed to Karbala to commemorate Sha'abaniya, the birthday next week of the Mehdi, the 12th imam revered by Shiites. The celebrations reach their peak on Tuesday night into Wednesday.
Separately, a U.S. military operation Sunday in Samarra, north of Baghdad, killed at least 18 insurgents, and the U.S. military is investigating reports that several Iraqi civilians were killed and wounded in a subsequent airstrike.
Samarra police said five civilians were killed and seven wounded in an airstrike on a house around 3 p.m. (7 a.m. ET).
Samarra police said the strike killed three children and two women, and wounded five other children, a woman and a man. E-mail to a friend
CNN's Arwa Damon, Jomana Karadsheh, Ed Henry and Raja Razek contributed to this report.