President Bush adopted the role of referee in the immigration debate yesterday, coaching a “civil” exchange on a topic that has not yet reached the Senate floor but is already roiling Congress.

Following a meeting with church, business, and immigration leaders, the president urged the nation’s lawmakers and “people who like to comment on this issue, to make sure the rhetoric is in accord with our traditions.”

The Senate majority leader, Bill Frist, has set Monday as a deadline for the Senate Judiciary Committee to come up with a bill for the Senate to consider. If it does not, he plans to push debate on his own bill, which would open no new avenues for immigrants to come legally to America, would clamp down on the border, and create harsh new enforcement measures.

The minority leader of the Senate, Harry Reid, a Democrat of Nevada, has retaliated, saying he would do everything, including a filibuster, to thwart legislation not cleared by the Judiciary Committee.

Yesterday, the president declared immigration a “vital debate for our country,” and urged senators to pass a bill that would include a guest worker program.

Secretary of Homeland Security Michael Chertoff spoke in New York yesterday about the deluge of illegal immigration America faces and the need for reform. “People rightfully are disturbed by the notion that we do not have control of the borders,” he said.

The last time Congress attempted comprehensive reform in 1986, he said it failed to keep out illegal immigrants. Instead, today there are between 8 and 12 million in America.

The solution he proposed, however, is not limited to a crackdown on the border and beefed-up internal enforcement, but the creation of new legal avenues. “We have to recognize that solving the problem is not easy, because the vast majority of illegal migrants who are crossing the border are coming for economic reasons,” he said.

A guest-worker program – first introduced as a possible solution by the president in January 2004 – would help stem some of the illicit market, Mr. Chertoff said. While America “cannot fight the wave of economic demand that is pulling people in,” he said more visas “will allow us to relieve some of the pressure on the border and to try and focus our resources on those who we’re really worried about.”

Left out of his discussion was how to rid the country of the 12 million illegal immigrants already here. The president has said no to an amnesty, but has been open to creating a way for illegal immigrants to gain legal status through an earned-legalization plan.

While most illegal immigrants go undetected, Mr. Chertoff said another problem is that after they are caught, their home countries often do not want them back.

“The results we’re looking for is not just to get them in jail, where we have to pay hundreds of dollars a week to keep them boarded and fed. The idea is to send them back to their home countries,” he said. “We can’t do that without the cooperation of the countries where they come from.”

China, in particular, has been reluctant to accept its illegal migrants. Mr. Chertoff has estimated that American authorities hold 19,000 Chinese illegal immigrants because their government has refused to repatriate them. On a trip to Asia later this month, he said a priority will be urging China to change its policy, as well as to crack down on the smuggling networks that bring illegal immigrants here.