Russian Foreign Minister Igor Ivanov, at a news conference with Albright, responded that Moscow had to move firmly against terrorism and that no one has come up with an effective recipe other than force.
"All our counterparts share the necessity to fight most firmly against terrorism," he said.
Albright appealed to Ivanov in an initial round of talks to open a dialogue with Chechen political figures, saying that otherwise Russia risked increased diplomatic isolation around the world.
Their open debate, at a joint news conference, underscored the ebb of U.S.-Russian relations, marked also by disagreement over a potential U.S. program for space-based weapons.
Philosophically, Albright said "these are unlikely to be given to one-day remedies" and that President Clinton is prepared to visit Moscow to continue the dialogue with acting President Vladimir Putin.
Albright's visit is designed to size up Putin, to push for an easing of restrictions on antimissile defenses, and to persuade him to change course in Chechnya.
In a small gesture of cooperation despite their differences, Albright and Ivanov took a break while tackling their heavy agenda to sign an agreement designed to tighten controls on technology used in launching U.S. satellites from Russian space stations.
"There is no question the war in Chechnya is popular," Albright told reporters on her flight Sunday night from Switzerland. "But he is riding a tiger" by pushing the military offensive against rebels in the republic.
Albright said casualties were mounting and that Russia faces more isolation in the international arena as the war drags on. "They have to hear over and over again that this is not working for them," she said.
Persistent U.S. appeals to Russian leaders to end the conflict and negotiate with the Chechnya separatists have failed. Albright did not predict success this time, either, and she ruled out U.S. economic sanctions if persuasion does not work.
Still, she said, "It is very clear to me that Russia is hurting itself because of Chechnya."
Albright also was primed to discuss with Putin sharp cuts in U.S. and Russian long-range nuclear arsenals while urging the Kremlin leader to approve "modest adjustments" in a ban on missile defenses.
And yet, the secretary said any idea of a tradeoff was "hypothetical" and that the United States would not negotiate a new treaty to reduce nuclear weapons stockpiles until the Russian parliament approved the 1993 START II accord.
Mr. Clinton is due to decide this spring whether to go ahead with a $6.6 billion program to launch a defense against missiles from such "rogue states" as Iran and North Korea.
He will make the decision based on U.S. national interest, Albright said. But she said she also would like Russia to modify a 1972 treat that banned such defenses against missiles.
By Barry Schweid
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