Bremer is also expected to hold talks with UN Secretary-General Kofi Annan on Monday in an effort to convince the United Nations to send staff back to Iraq to help with the transition process.
A US plan for a handover of power by July has run into stiff opposition from Iraq's top Shia cleric Ayat Allah Ali al-Sistani, a Kurdish drive for autonomy in the north and a warning of bloodshed from a leader of the minority Turkmen.
Bremer's talks at the White House on Friday would cover "the political dynamic (in Iraq), the ongoing discussions with Sistani and the Kurds", said a US official.
Sistani has objected to the US plan for a transitional assembly to be selected by regional caucuses. The assembly will choose an interim government for sovereignty by the end of June. Full elections are due to follow next year.
Winning over Sistani
Bremer has said he respects Sistani but that there is not enough time to hold elections before a handover of sovereignty due to lack of electoral registers and polling laws.
US officials say they are reviewing the planned regional caucuses to make the process as open as possible.
Tens of thousands of Iraq's Shia Muslims marched on Thursday through Basra to chants of "No to America" on Thursday and an aide to the Shia spiritual leader warned of wider protests if the long-oppressed group's demand for elections was not met.
"If (Sistani) issues a fatwa (edict) all the Iraqi people will go out in protest marches and demonstrations against the (US-led) coalition forces," an aide to the cleric, Ayat Allah Muhammad Baqir al-Mohri, told reporters in Kuwait.
Thousands marched in support
of Sistani's call for early polls
Mohri earlier told an Arabic TV station that such a fatwa could undermine the legitimacy of any unelected Iraqi administration.
A Sistani edict could turn many Shia against Washington at a time when US-led forces are battling guerrillas in the Sunni Muslim areas north and west of Baghdad, the heartland of support for Saddam Hussein.
US officials and the US-appointed Iraqi Governing Council were trying to persuade Sistani to soften his stance.
Adding to tensions in Iraq, the country's Arabs and Turkmen bitterly oppose a plan by Kurds on the Governing Council for significant autonomy for a Kurdish area in the north.
"We will defend the unity of Iraq until the last moment and the last drop of our blood," said Sami Muhammad Donmez, deputy leader of the Iraqi Turkmen Front coalition of parties.
The United States and the Governing Council are pushing for the United Nations to play a role in the political transition by overseeing the regional caucuses.
If (Sistani) issues a fatwa (edict) all the Iraqi people will go out in protest marches and demonstrations against the (US-led) coalition forces"
Ayat Allah Muhammad Baqir al-Mohri, an aide to Sistani
Abd Al-Aziz al-Hakim, a Shia Muslim on the Governing Council, wrote to Annan asking the United Nations to study the possibility of early polls or find a compromise path to election of an assembly.
Annan said in reply it was technically impossible to organise elections by June. He stopped short of promising UN action in solving the dispute or endorsing the current process.
Bremer will be joined at Monday's talks with Annan by Governing Council members and representatives from the United States and Britain.