The US administrator in Iraq, Paul Bremer, has played down differences with the majority Shia population over the transfer of power to the Iraqis.
New threats of action were made during Friday prayers
He was speaking after talks with President George W Bush in Washington.
The spiritual leader of Iraqi Shias, Ayatollah Ali al-Sistani, is demanding direct elections before the transfer of power at the end of June.
Earlier a White House official hinted that "refinements" or "improvements" could be made to the handover plan.
Mr Bremer echoed that view, saying: "We've always said we're willing to consider refinements and that's something that we will be willing to discuss at the appropriate time."
The meeting in Washington came a day after a mass demonstration in the southern city of Basra in support of the demands of Ayatollah Sistani.
At Friday prayers a spokesman for the ayatollah threatened general strikes or even clashes with coalition forces if the US persists with it.
Correspondents say the support of Shias is vital for any new Iraqi government to have legitimacy.
Mr Bremer said he had "the greatest respect" for Ayatollah Sistani and that there was a great deal on which they agreed, including that Iraq should move towards a democratic form of government.
He denied that there was a fundamental disagreement between them, saying: "I don't think that's true."
Mr Bremer is expected to press for UN support during a high-stakes meeting with Secretary General Kofi Annan and members of the US-appointed Iraqi Governing Council on Monday.
Shias were long repressed by Saddam Hussein and they want more open elections to reflect their numerical superiority, correspondents say.
The strongest challenge yet to the coalition came during Friday prayers in the holy city of Karbala from Sheikh Abdul Mahdi, the local representative of Ayatollah Sistani.
He told followers: "In the next few days, we will see protests, strikes and may be clashes with the occupation troops if they insist on their colonialist scheme and on
designing Iraq's policy according to their own interests."
POWER TRANSFER TIMELINE
Feb 2004: Fundamental Law (provisional constitution) to be introduced
May, 2004: Selection of Transitional National Assembly (TNA)
June 2004: TNA to take power; Coalition Authority and Governing Council to dissolve
March 2005: Constitutional Convention elected to draft new constitution
Dec 2005: New constitution; elections and appointment of new government
The BBC's Dumeetha Luthra in Basra reports that another Sistani aide said the ayatollah could issue a fatwa, banning co-operation with coalition forces.
On Thursday Hojat al-Islam Ali Abdulhakim al-Safi, the second most senior Shia cleric in Iraq, sent a letter to President Bush and UK Prime Minister Tony Blair accusing them of delaying full elections to serve their own purposes.
The US has said it welcomes Iraqi protests as a natural by-product of the new freedom in the country, but insists that security problems and incomplete voter records make the holding of general elections impracticable for now.
But the ayatollah's implacable opposition places the US in the difficult position, according to the BBC's Justin Webb in Washington.
Mr Bremer will face another crucial meeting on Monday when together with Adnan Pachachi, the head of the Iraqi Governing Council, he is set to ask UN Secretary General Kofi Annan to send UN representatives back to Iraq to participate in the transition.
Mr Annan, who pulled United Nations staff out of Baghdad after a massive car-bomb attack on UN offices last August, has said the UN could help but only if given a role commensurate with the risks involved.