Washington ? Even as the war continues in Iraq, a broader and ultimately more important political struggle is under way in Washington over the future government of that country — and of America’s relations with the world.

“This is the big one,” Sen. Joseph Biden of Delaware, the senior Democrat on the Foreign Relations Committee, told me. And there are many other serious students of international relations who share that view and are taking up positions in the battle.

Two things are clear. When Saddam Hussein’s regime is defeated — and everyone hopes that will be soon — the American-led and American-dominated military forces will have the responsibility for security in Iraq for some indefinite time — months, if not years. And the United Nations must have an equally important role in supervising the delivery of food, medicine and other humanitarian assistance to the battered people of Iraq. The U.N. Security Council voted unanimously last week to prepare for that responsibility.

What remains in doubt is the character of the civil administration that will manage the transition to an eventual post-Saddam government that will be representative of the Iraqi people.

Democratic Rep. Ron Kind of Wisconsin and Republican Rep. Doug Bereuter of Nebraska, both well-regarded if not widely known voices on international affairs, last week quickly collected the signatures of 42 colleagues on a bipartisan letter urging the Bush administration to seek U.N. involvement in creating a new Iraqi government.

Their move parallels the unanimous passage last week by the Senate of a resolution, written by Biden and Foreign Relations Committee Chairman Richard Lugar of Indiana, welcoming the participation of “other nations and key international organizations in the reconstruction and administration of Iraq.”

The messages from Capitol Hill are aimed at influencing what Kind called “a raging debate” inside the Bush administration. The immediate question is whether postwar Iraq will be run by an American viceroy or a U.N. official. But the larger question is whether superpower America will seek to heal the breach with longtime allies that blocked U.N. action against Saddam Hussein, or walk away from the world body and seek to manage future conflicts with its own “coalition of the willing.”

The Pentagon, which holds the upper hand in that debate because it is calling the shots in the war, already has designated a general to take over at least temporarily in Baghdad. Biden, who is blunt in his appraisal of the stakes, told me that he thinks Defense Secretary Donald Rumsfeld and Vice President Dick Cheney are “seeking a twofer. They want to get rid of Saddam Hussein and break the grip of the United Nations.”

Kind is slightly more tactful in his description, but said that, judging from his sources in the State Department, “This is the issue of the day. It will affect our relations with the Arab nations and the rest of the world for decades to come. And it has a direct bearing on our security. As powerful as our military is, if we’re seen as the occupying power in a Moslem country, it makes us more vulnerable to terrorism.”

Biden, in a Senate floor speech, said an international structure is needed in Iraq, not just to reduce the threat of retaliatory attacks on the United States, but to spread the huge financial burden of rebuilding that country and “to repair the damage that has been done to the U.N., to our alliances and international cooperation” by the decision to launch this war over the opposition of France, Germany, Russia and many other countries.

Any new government in Iraq, Biden said, needs “the imprimatur of the international community. The last thing we need to do is look as though we are putting in a puppet government.”

As is often the case, no one is quite certain where President Bush stands in this debate. The hard-liners inside and outside the administration — the same people who pressed for taking on Saddam Hussein — are arguing that the U.N. showed its true colors when it refused to enforce its own ultimatum to Iraq — so the hell with it. But Bush’s staunchest ally, Britain’s Tony Blair, the State Department and now a significant group of internationalists in Congress who supported the resolution authorizing the use of force against Iraq all are pressing Bush to invite the U.N. and other nations to share the postwar duties in Iraq.

Looming ahead are the global war on terrorism, challenges from nuclear threats in North Korea and Iran, and the bloody impasse of the Palestinian-Israeli struggle. For the United States to go it alone would be a fateful decision.

David Broder is a columnist for Washington Post Writers Group.