Laurent Fabius, who will preside over the November 30-December 11 conference in Paris, told journalists the three days of talks ending today had been an important step and "progress has been made on at least five points".
Nevertheless, he said, "the task ahead is considerable".
UN climate chief Christiana Figueres added: "It continues to be entirely possible to come to an agreement... Despite all the challenges in front of us."
A rough draft of that hoped-for agreement has been drawn up by rank-and-file diplomats, with ministers set to sign the final deal at the end of the Conference of Parties (COP) in Paris.
The deal will be underpinned by national pledges to curb greenhouse gas emissions from burning fossil fuels blamed for climate change.
Fabius said there was momentum toward ensuring that countries ratchet up their efforts to slash carbon pollution beyond pledges submitted ahead of the summit.
"A review should take place every five years... To prepare an upward revision of national plans," he said.
Current national plans would yield average global temperatures three degrees Celsius above pre-industrial times -- far beyond the 2 C (3.6 degrees Fahrenheit) limit that scientists say is the threshold for dangerous warming.
Enshrining the principle that nations would not be allowed to "backtrack" on their carbon-cutting promises is also gaining ground, Fabius said.
Another make-or-break issue on the table in the three-day talks: chanelling money to developing nations to help them decarbonise their economies, and to shore up defences against unavoidable climate impacts.
"Climate finance was very central" to the discussions, said Thoriq Ibrahim, Minister of the Environment and Energy for the Maldives, one of many small island states whose very existence is threatened by rising seas.
The 195-nation UN climate forum has officially adopted the goal of limiting global warming to 2 C, but many vulnerable and poor nations are pushing for that threshold to be lowered to 1.5 C.
Recent scientific studies have shown that even if the 2 C goal is attained, the impact could be devastating in many parts of the world.
A 2 C spike would submerge land currently occupied by 280 million people, while an increase of 4 C -- humanity's current trajectory -- would cover areas home to 600 million, according to a study published by Climate Central, a US-based research group.
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