While major museums and archaeologists agree that the looting of ancient sites is deplorable, they have reached little consensus of how best to stop it – despite more than seven hours of scholarly presentations, impassioned speeches, and pointed debate.

Following months of public dispute over the ethics of collecting antiquities, museum leaders confronted their chief critics in a day-long conference yesterday that was spirited but civil. Ultimately, the scholars gathered at the New York Public Library centered on a single question of practicality that seemed to crystallize their philosophical differences: What should museums do when offered a valuable object whose complete provenance is unknown?

To those who support the position of the Archaeological Institute of America, the rejection of that object is key to curtailing the market that encourages the looting and destruction of ancient sites. “In most of these cases, these things are stolen property. There’s no other way to call them. They are stolen property,” a panelist who is a cultural property law expert at DePaul University, Patricia Gerstenblith, argued. Ms. Gerstenblith suggested that museums alert the police when they are offered questionable objects for purchase.

Museum officials took the opposite view, suggesting that to refuse unprovenanced objects out of hand would solve nothing and risk losing a key piece of cultural history in the process.

The question arose throughout a forum that museum directors organized largely to offer a defense of their institutions, which they claim have unfairly come under attack in the midst of investigations and trials that have uncovered a vast illicit trade in antiquities.

As museums defended themselves yesterday, so did their opponents. The president of the archaeological institute, Jane Waldbaum, disputed suggestions that she represented, in her words, “a small minority of lunatic, fringe” scholars.

While Ms. Waldbaum and her colleagues said museums should curtail collecting out of moral and legal necessity, museum directors questioned the cultural property laws that restrained the market in the first place. The laws, they said, had proved ineffective in preventing looting and only drove the market further underground.

Afterward, the two sides disagreed even on the outcome of the conference. The director of the Art Institute of Chicago and an organizer of the symposium, James Cuno, said that while clear differences remained, he saw progress toward bridging the gulf between museums and their critics. Archaeologists, however, said little was accomplished. “I was really surprised at how much they dislike archaeologists,” a panelist and a vice president of the archaeological institute, Malcolm Bell, said.