COPENHAGEN — Delegates converged Sunday for the grand finale of two years of tough, sometimes bitter negotiations on a climate change treaty, as U.N. officials calculated that pledges offered in the last few weeks to reduce greenhouse gases put the world within reach of keeping global warming under control.

Yvo de Boer, the U.N.’s top climate official, said on the eve of the 192-nation conference that despite unprecedented unity and concessions, industrial countries and emerging nations need to dig deeper.

“Time is up,” de Boer said. “Over the next two weeks, governments have to deliver.”

Finance — billions of dollars immediately and hundreds of billions of dollars annually within a decade — was emerging as the key to unblocking an agreement that would bind the global community to a sweeping plan to combat climate change.

Nations also must need to commit to larger emission reductions, de Boer said.

South Africa on Sunday became the latest country to announce an emissions target. It said over the next 10 years it would reduce emissions by 34 percent from “business as usual,” the level they would reach under ordinary circumstances. By 2025 that figure would peak at 42 percent, effectively leveling off and thereafter begin to decline.

More than 100 heads of state and government have said they will attend the last day or two of the summit.

“Never in the 17 years of climate negotiations have so many different nations made so many firm pledges together,” de Boer said.

A study released by the U.N. Environment Program Sunday indicated that pledges by industrial countries and major emerging nations fall just short of the reductions of greenhouse gas emissions that scientists have said are needed.

“For those who claim a deal in Copenhagen is impossible, they are simply wrong,” said U.N. Environment Program Director Achim Steiner, releasing the report.

All countries together should emit no more than 44 billion tons of carbon dioxide by 2020 to avoid the worst consequences of a warming world, the U.N. report said.

Computing the high end of all commitments publicly announced so far, the report said emissions will total about 46 billion tons annually in 2020. Emissions today are about 47 billion tons.