Just when the dust started to settle over recent difficulties at the United Nations, another tiff began brewing Tuesday over humanitarian aid in Iraq.

Some members of the Arab League and the non-aligned movement have demanded that a public debate take place Wednesday on the conflict in Iraq. The United States has said that's a non-starter, though whether it can stop a discussion remains to be seen.

Instead, U.S. and British diplomats have said the first order of business for the international body needs to be planning for the delivery of humanitarian aid to the war-ravaged populace in Iraq. British officials said they would be amenable to other discussions after assistance is sorted out.

National Security Adviser Condoleezza Rice was meeting with Secretary-General Kofi Annan on Tuesday to discuss that assistance.

Officials have said they are hoping to restart Iraq's oil-for-food program, which already has several billion dollars of oil in the pipeline. Debate has been percolating over who would take the U.N. humanitarian aid and distribute it.

The United States wants to convince the Security Council to turn over administration of the oil-for-food program to Annan for the near term, and eventually to the Iraqi people. Annan has asked that the outline for this be put into a Security Council resolution.

"Somebody needs to be able to come forward and say, 'okay, this is what they need now. This ought to go here. This is a higher priority than something else, and this is how we should spend the money right now," said State Department spokesman Richard Boucher. "So the conceptual framework is that the secretary general is needed for the immediate and perhaps transitional period, but that as soon as possible would want to get Iraqis involved in running the program and eventually in running an economy that doesn't require the program."

The United States and Britain have also said they would like a Security Council resolution to authorize civilian authority in Iraq, but France and Russia contend any such a document would legitimize the U.S.-led war effort that they so adamantly opposed this month.

Britain and the United States, along with Security Council members Spain and Bulgaria, last month failed to get a second war resolution to complement Resolution 1441, passed last November and calling for "serious consequences" if Iraq doesn't comply with demands for immediate disarmament.

A second resolution would have provided additional U.N. cover for military action in Iraq, but veto-wielding members France and Russia, and another member, Germany, all balked at a second resolution, demanding more time for Iraq to comply. That forced the coalition partners to withdraw the request, saying that Resolution 1441 offered enough legal authority to allow them to launch a war.

Now as the debate moves to something completely different, some U.N. members are questioning who can deliver the necessary humanitarian aid, a source told Fox News.

Some members have suggested that as an "occupying power," the U.S.-British-led coalition has certain responsibilities.

While U.S. and British officials said they are perfectly willing to live up to the responsibilities they have already offered, they take issue with the characterization of them as an occupying power in as much as they don't occupy or control the entire country.

As coalition members look for ways to bring in aid, some U.N. members are also bickering over how it will take shape. One diplomatic source said the Russians are filibustering, saying they don't want any language that necessarily refers to "relevant authorities" because they want to make sure that refers to an Iraqi government itself.

Russian officials have said they also want some compensation for companies -- presumably Russian -- that might be hurt because of contracts that could be disrupted by the war. They did not indicate whether that included companies that allegedly have sold GPS jammers and other equipment to Iraq in violation of U.N. sanctions.

At a Pentagon briefing Tuesday, Defense Secretary Donald Rumsfeld said humanitarian assistance -- "food, water and medicine" -- is already being delivered.

Iraqis in Basra are most in need of aid as the water supply has been cut off for as long as five days. British forces have set up loudspeakers around the city to tell Iraqis where to go for humanitarian aid, but that aid is slow in coming because coalition forces are still sweeping the deep water port of Umm Qasr for mines before they allow aid ships to come in.

Officials had hoped for agreement Tuesday on procedures for starting up aid, but it now looks like any agreement won't come until the end of the week at the earliest.

Asked what role the United Nations might play in the reconstruction of Iraq, one official said, "Too far down the road."

Fox News' Jim Angle and Teri Schultz and the Associated Press contributed to this report.