BAGHDAD — Attempts to pass a key oil law sought by the American government were snarled once more yesterday by deep differences among Iraq’s Sunni, Shiite, and Kurdish leaders, delaying Parliament debate despite the prime minister’s claims of a breakthrough.

Despite heavy American pressure, Prime Minister al-Maliki has struggled for months to get members of his coalition together behind the bill, part of a long-delayed political package that the Bush administration hopes will reconcile Iraq’s Sunni Arab minority with the government, reduce support for the insurgency and ease the country’s violence.

Parliament failed to start debate on the bill yesterday, despite Mr. Maliki’s announcement the day before that it would. The acting speaker, Khaled al-Attiya, said he expected it to be sent today to the legislature, where it would be put to a committee.

Mr. Maliki said Tuesday that his Cabinet had unanimously approved a draft of the law, raising hopes that major progress had been made — President Bush phoned the prime minister to thank him for the step. But almost immediately Sunni and Kurdish members of his coalition said they were not yet on board.

The influential Sunni organization, the Association of Muslim Scholars, issued a fatwa, or religious edict, blasting the bill as “religiously forbidden” and warned that those who back it “anger God for usurping public money.”

The wrangling over the bill is so tough because it hits on the most contentious question over the future shape of Iraq — how to balance power between the central government and the country’s regions, divided on sectarian and ethnic lines. The demands of each side — Shiite, Sunni, and Kurdish — for the bill are far apart, and often mutually exclusive.

The law aims to regulate Iraq’s oil industry and will determine the central government’s role, and companion legislation that is nearly finalized sets how oil wealth will be distributed among regions.

Sunnis, centered in parts of the country with few proven reserves, fear Shiites and Kurds in the oil-rich south and north will monopolize profits from the industry — and so want a stronger federal role to ensure a Sunni say in how the fields are run.

The Kurds, in particular, want control of potentially lucrative future discoveries of reserves in their northern enclave.

Further complicating the negotiations are other political disputes.

Mr. Maliki’s main Sunni coalition partner, the Iraqi Accordance Front, was not present when the Cabinet approved the draft because it is boycotting meetings in a row over an arrest warrant issued against the Sunni culture minister. An Accordance Front leader warned yesterday that no draft should be considered until the Sunnis sign on.

Mr. Maliki may have pushed the bill through the Cabinet in an attempt to force the Accordance Front to end its boycott.

But the Kurds also objected, fearing concessions had been made to the Sunnis. The Kurdistan Regional Government warned it would oppose the bill if it made “material and substantive changes” to an outline agreed upon during weeks of negotiations.

Meanwhile, the Shiite party loyal to anti-American cleric Moqtada al-Sadr, which opposes too much decentralization, outright rejected the draft, saying it “left nothing of Iraq’s unity.”

The oil bill is the first of the political benchmarks that Bush has pressed Mr. Maliki to meet, along with opening jobs to Sunnis who supported Saddam, amending the constitution to satisfy Sunni aspirations and holding local elections. The Iraqis pledged to meet the benchmarks by the end of last year but failed due to political haggling and the security crisis.

Besides bringing together Iraqis, American officials are also hoping progress on the benchmarks will show the American public — where support for the war is dropping — that Mr. Bush’s strategy is working.

Mr. Bush ordered 28,000 more American troops to Iraq this year to launch security crackdowns in Baghdad and north and south of the capital aimed at tamping down insurgents enough to allow political agreement.

The offensives have boosted American casualties, although the number of bombings and shootings has fallen in the city in recent days.

As American troops in some bases marked the July 4 holiday, two American soldiers were killed during separate incidents, including one who died when a helicopter “went down” in Nineveh province north of Baghdad, the American military reported.

The second fatality occurred during combat operations in south Baghdad, the military said without giving further details.

A brief statement by Multinational Corps-Iraq said another soldier was wounded in the helicopter incident and was transported to an American military hospital. The statement did not explain why the helicopter went down or whether it was involved in combat operations.

American forces killed 10 insurgents in a raid yesterday on a suspected Al Qaeda hideout in western Anbar province, the military said in a statement.