The Bush administration is taking a fresh look at its plans to turn over power in Iraq by June 30.

While that remains the deadline, Defense Secretary Donald H. Rumsfeld (search) said Tuesday it's too early to tell whether it will have to be changed.

The review under way is in response to objections to parts of the current plan by a leader of Iraq's majority Shiite Muslims. The search for a compromise is under way within the administration and in quiet discussions with prominent Iraqis.

Grand Ayatollah Ali al-Husseini al-Sistani (search) demanded this week that any agreement to lnt U.S.-appointed Iraqi Governing Council (search) agreed last November that the next government could be chosen in regional caucuses, not full-scale elections.

The decision to turn over control to Iraqis by June 30 remains a constant goal, administration officials said. It was not clear how the goal could be sustained, however, if a compromise cannot be reached with the Shiite (search) leader.

"It's too early to tell," Rumsfeld said. "There are going to be ups and downs and zigs and zags in the road."

What has to be worked out, he said, is whether it's more important to have elections and delay transfer of sovereignty to Iraqis or to transfer sovereignty and have elections afterward in support of the power shift.

One idea under consideration is to hold a referendum on transferring control, a U.S. official said on condition of anonymity.

Looking for help, the State Department said the United Nations, with its expertise in setting up and monitoring elections, could send a delegation to Baghdad to help find a solution.

The U.N. role in Iraq will be explored next Monday in New York with Secretary-General Kofi Annan presiding at a meeting with U.S. and Iraqi officials. The chief U.S. administrator in Baghdad, L. Paul Bremer, probably will head the U.S. delegation.

Discussions already under way in Washington and with Iraqi leaders involve the possibility of opening up a series of planned caucuses in Iraq in ways that permit wider participation, the officials said.

Hovering over the transition are questions about how diverse an Iraqi government would be.

The Shiites are thought to have a 60 percent majority, although Bremer questioned that estimate Tuesday since Iraq has not had a census in almost two decades.

Bremer acknowledged the Shiites eventually might control over the country, as the sect does in next-door Iran. "In a democracy it's axiomatic that the majority will rule," Bremer said on NBC's "Today."

The current U.S. plan, now being reconsidered for fine-tuning, would have caucuses around the country select an interim legislature and executive in a newly self-governing Iraq.

The first formal national elections would not be held before March 2005.

Al-Sistani demanded Sunday that the provisional assembly, which would pick an interim government, be chosen by national elections.

He also said the assembly should ratify an interim constitution, being drafted by the Iraqi Governing Council, and rule on whether U.S. and allied troops could remain in Iraq after July 1.

Bremer said the administration agrees with the ayatollah that it is important to have an elected assembly write a constitution, and he said that would happen in about a year.

But Bremer saw technical and mechanical problems with having early elections. Among them, he said, would be that Iraq has no electoral and political party laws, and it would take months to set up an election.

"We don't have that much time until we transfer sovereignty in accordance with the will of the Iraqi people," Bremer said.

The administrator acknowledged on CBS' "The Early Show" that the caucus method was not as good as an election but said the caucus method would bring about an effective and representative government.

The administration last November designed its plan for transition to Iraqi rule under pressure from the United Nations and from critics of the war to depose President Saddam Hussein.

Still, the administration is determined to keep U.S. troops in Iraq to help in the transition. Nearly 500 have been killed, but Bremer told Fox News that the attacks are down since Saddam was captured in mid-December.

More than 100,000 U.S. troops still are in Iraq. The aim is gradually to shift security responsibilities to Iraqis currently in training.