COPENHAGEN, Denmark - If the talks that resulted in an imperfect deal to combat global warming provided anything, it was a glimpse into a new world order in which global diplomacy will increasingly be shaped by the United States and emerging powers, most notably China.

Friday's agreement, sources involved in the talks said, boiled down to President Obama and Chinese Premier Wen Jiabao personally hammering out a pact they could live with, even if many other nations could not.

What Obama heralded as a "breakthrough" - after getting India and other rising powers to sign on - was decried by some leaders as too little, too late. The leaders of Europe, Japan, and other countries at the summit were largely left to rubber-stamp the deal. The Swedish prime minister's office dubbed it "a disaster."

Ever since the concept of a Group of Two was proposed this year by former national security adviser Zbigniew Brzezinski, it has been pooh-poohed by both American and Chinese officials. China hated the notion of addressing the world's problems alongside the United States, because it put too much responsibility on a country that has done very well rising in the shadows. Many U.S. officials opposed it on the grounds that the best way to influence China was through multinational partnerships.

More than anything else, critics said, Friday's climate agreement reflected the domestic political realities in Washington and Beijing. Both nations, the two biggest emitters of greenhouse gases, remain more cautious than, say, the governments of Europe about establishing a strict set of rules to combat global warming. Not coincidentally, the agreement allows nations to set their own emission-reduction targets and provides no deadline for signing a binding international accord.

As such, the deal may portend how issues from world trade to nuclear proliferation will be negotiated in the years ahead, with China leading a caucus of rising powers on one side and the United States on the other.

"The mark is being stamped on a new political world," said Duncan Marsh, who directs international climate policy for the Nature Conservancy.

Orville Schell, a longtime China watcher who is director of the Center on U.S.-China Relations at the Asia Society, said the erratic dance between China and the United States was another example of how the bilateral relationship was at a tipping point. China is becoming a major player, albeit reluctantly; the United States, with similar uneasiness, is making room for China at the table of world leadership.

"We're not exactly partners, but we're much more equals," Schell said. "The Chinese miss the idea that there's some grander, stronger authority. They are not used to this role of actually helping to fashion and form things."

Indeed, the events at the summit showed how the U.S.-China relationship remains stormy and complex, constructive and adversarial. At one point in Friday's tense talks, for instance, China's top climate-change negotiator exploded in rage at U.S. pressure after Obama walked in on the Chinese while they were holding talks with the Indians, South Africans, and Brazilians. After Obama asked whether the Chinese could commit to listing their climate targets in an international registry, Xie Zhenhua launched into a tirade, pointing his finger at the U.S. president.

The United States had made any deal contingent on international verification of emission cuts made by nations, seeing it as key to winning over lawmakers on Capitol Hill still resistant to sweeping climate-change legislation at home. But there was no way China would agree to international verification, Xie told the Americans.

It was a position that China had held to closely over months of negotiations with the United States and other countries. China's vice minister of foreign affairs, He Yafei, had reiterated it just hours earlier.

But this time, something different happened, according to Chinese and Western sources close to the talks. Wen instructed his Chinese interpreter not to translate Xie's fiery remarks. When Xie erupted again, Wen, who was chairing the meeting, ignored him. After Wen handed Obama a draft text of an agreement that included verification language Obama couldn't abide by, the two men led a lengthy debate that ended in a working compromise, sources said.