A final text to conclude the summit has yet to be agreed upon, with outstanding issues including the creation of a new fund for reparations.
Climate negotiators have been grappling for an agreement at the UN Climate Change Conference (COP27) in Egypt, as talks remain hung up on key issues including funds for the "loss and damage" suffered by poorer vulnerable countries hit by extreme weather.
The extended negotiations on Saturday saw disagreements continue over who pays and which countries are considered particularly affected.
"The issue now rests with the will of the parties. It is the parties who must rise to the occasion and take upon themselves the responsibility of finding the areas of convergence," Sameh Shoukry, president of the COP27 climate summit, said.
Earlier, EU climate policy chief Frans Timmermans warned the bloc was "prepared to walk away" from the negotiations if a satisfactory outcome could not be reached.
"We'd rather have no decision than a bad decision," Timmermans told reporters on the sidelines of the summit, but said the EU still believed a deal could be struck on Saturday.
'Vast majority' says draft is 'balanced'
The EU statement came after a proposal from summit host Egypt was rejected as insufficiently ambitious on reducing carbon emissions.
Shoukry, however, said "the (draft) text does keep the 1.5 alive," referring to the aim already enshrined by previous climate summits to keep global warming to 1.5 degrees Celsius above pre-industrial levels.
"The vast majority of the parties indicated to me they considered the text as balanced and that they constitute a potential breakthrough that can lead to consensus," Shoukry also told journalists.
Meanwhile, UK and several other countries have reportedly circulated a new draft proposal document, which suggested the fund could be part of a range of "funding arrangements" and that the new source of monies could be operationalised in two years.
For many vulnerable countries, loss and damage is the defining issue of the conference, with some saying the success of the meeting hinges on the creation of a specific fund at the Egypt talks.
Wealthy nations had long been reluctant to discuss the issue over fears of liability until COP27.
They are also under pressure to finally fulfil promises to provide $100 billion a year to help developing countries green their economies and adapt to future impacts.