WASHINGTON — A political crisis in Baghdad came closer to ending yesterday after the decision of Adnan al-Duleimi to resign as the head of the Sunni-dominated Iraq Accordance Front — which also called the Tawafuq Party.

The crisis kicked off last Friday when Tawafuq ministers, encouraged by Mr. Duleimi, threatened to boycott the government following the issuance of an arrest warrant for Iraq’s culture minister — Asad Kemal al-Hashemi, a Tawafuq bloc member — for the murder of the two sons of a rival parliamentarian, Mithal al-Alusi.

Mr. Hashemi then fled to al-Rashid Hotel, inside the American-protected Green Zone, where American contractors prevented Iraqi police from entering the hotel’s compound to arrest the minister. Mr. Hashemi is now believed to be in Jordan.

Yesterday, the Tawafuq Party announced that Mr. Duleimi, who is also believed to be in Jordan, will no longer be its leader. The job now goes to Ayad al-Samarraie, who is considered a more moderate voice, particularly on sectarian matters. The leadership change may pave the way for Tawafuq’s 44 legislators to participate in Parliament, which will make it possible to hold a vote on sections of a draft oil law that the American Embassy considers one of its three pillars for achieving political reconciliation in Iraq.

Yesterday, Mr. Samarraie said the participation of ministers and parliamentarians in the government were separate matters. “The matters are different because our return to Parliament is linked to the return” of the speaker of Iraq’s Parliament, Mahmoud al-Mashhadani, “and our return to the Cabinet will be after an arrest warrant against Minister Asad al-Hashemi is withdrawn. These matters cannot be mixed,” he told the Associated Press.

Meanwhile, Mr. Hashemi, now accused of ordering and financing the 2005 murder of Ayman and Jamal al-Alusi, has been spotted in Jordan by members of Jordanian intelligence, according to an American intelligence official who said the report was passed on to the CIA.

For his part, Mr. Alusi said yesterday that Iraq’s police are demoralized. “The Iraqi National Police are very sad,” he said. “The politicians leave them alone, the government tried to hide.”

At the same time, Mr. Alusi said he has received a lot of support in his struggle for justice for the murder of his sons. According to Mr. Alusi, there are thousands of dormant cases in Iraq’s overburdened justice system against members of the personal security details of both Sunni and Shiite politicians.

Mr. Alusi caused a stir in Baghdad last week by accusing the American Embassy in Baghdad — on national television — of effectively harboring Mr. Hashemi when they refused to order the security contractors at the gate of al-Rashid compound to allow the national police to enter. The State Department has denied any command responsibility for the contractors at the gate of al-Rashid compound.

“If he left, he must have a clearly strong network and a false passport,” Mr. Alusi said yesterday. He added that Iraq’s border guards and security at the international airport have no record of the culture minister passing through.

“Big people gave him help,” Mr. Alusi said. “I was in the al-Rashid Hotel, the first day, the security people are very nervous. But yesterday, I was there for a meeting, and everything was very quiet and very normal.”

The Tawafuq Party has long been under scrutiny from Iraq’s Shiite-dominated military and security services. As The New York Sun reported in May, the chief general in charge of the Baghdad Operations Command has recommended that 15 members of Tawafuq be prosecuted for involvement in terrorism. One of those legislators, Khallad al-Ayan, is believed to have provided the explosives for the suicide bomber that killed one of his party’s own parliamentarians in April.

Mr. Ayan has not been seen in Iraq since Iraqi and American military men raided his home and Parliament offices in April.