After talks resumed in the afternoon, the Tuvalu delegation walked out when it appeared that the issue might be sidelined.
Private discussions will now continue behind the scenes among a small group of concerned countries.
Tuvalu's negotiator Ian Fry made clear that his country could accept nothing less than full discussion of its proposal for a new legal protocol, which was submitted to the UN climate convention six months ago.
"My prime minister and many other heads of state have the clear intention of coming to Copenhagen to sign on to a legally binding deal," Mr Fry said.
"Tuvalu is one of the most vulnerable countries in the world to climate change, and our future rests on the outcome of this meeting."
Demonstrators protest in support of Tuvalu's proposal
The call was backed by other members of the Association of Small Island States (AOSIS), including the Cook Islands, Barbados and Fiji, and by some poor African countries including Sierra Leone, Senegal and Cape Verde.
Several re-iterated the demand of small island developing states that the rise in the global average temperature be limited to 1.5C, and greenhouse gas concentrations stabilised at 350 parts per million (ppm) rather than the 450ppm favoured by developed countries and some major developing nations.
Fast-growing economies such as China, India and South Africa oppose the lower target of 350ppm because they feel that meeting it would retard economic development.
Here, they also opposed Tuvalu's call for a new legally-binding protocol to run alongside the existing Kyoto Protocol, arguing that the existing convention and Kyoto agreement are tough enough.
"The main task of this (conference) is to adapt an agreed outcome from the Bali Action Plan [agreed in 2007] and we should very much focus on that," said China's lead negotiator Su Wei.
"We have a very valid system to combat climate change."
But the existing agreement is not tough enough for the smaller, more vulnerable members with more to lose from rising sea levels and less to lose in terms of the economic constraints of a tough treaty.
China's negotiator Su Wei told the conference that his country, and the other emerging economies, did care about the problems of small island states; but Jerome Esebei Temengil from Palau's delegation gave a different view.
"We're dying here, were drowning; and some of us know that they don't really care, because we have to beg them," he told BBC News.
"Actions speak louder than words. If they really do care, please have a little listen to us."
Some observers suggested the session marked a major development in the politics of the climate convention, with small countries prepared to stand up to more powerful neighbours.
"This is the first time we've seen the island nations make such a splash," said Malini Mehra of the India-based Centre for Social Markets.
"The AOSIS call for a new protocol and the way it was denounced by Saudi Arabia, China, and India show that the G77 has now come asunder and the island nations are leading," she told BBC News
"As they must - they have seized the high moral ground."
During the same session, China - and other countries - re-iterated calls for industrialised nations to pledge bigger cuts in their greenhouse gas emissions.
But that has been a familiar call here; the rift between members of the formerly solid developing country bloc is a much less common happening, and may indicate that hopes held out by some countries of signing only a political commitment here may not be enough to placate the poorest and most vulnerable nations.
China has protested against an incident which prevented a top diplomat from entering the vast Bella Center where the conference is underway. Mr Wei told the meeting he is "extremely unhappy" that a Chinese minister was barred from entry on three consecutive days.
He said the unnamed minister has been trying to enter since Monday but failed despite having two security badges made out. Both badges were confiscated by security guards on Wednesday morning.
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