The theory that an abrupt, catastrophic change in the climate extinguished the last Neanderthals is challenged in the journal Nature.
Our evolutionary cousins went extinct in most of Europe about 35,000 years ago, but small pockets survived much later than this in southern Iberia.
The cause of these ancient humans' demise is hotly debated and a variety of theories have been put forward.
However, other researchers question the study's conclusions.
Neanderthals (Homo neanderthalensis) first appear in the fossil record about 230,000 years ago and, at their peak, ranged across Europe and parts of western Asia.
Competition with modern humans (Homo sapiens) - who arrived on the European continent about 40,000 years ago - as well as climate change, have long been discussed as culprits for the Neanderthals' extinction across much of their former range 35,000 years ago.
But pockets of these ancient humans appear to have survived in southern Iberia until much more recently than they did elsewhere - perhaps until 24,000 years ago.
Climate change is proposed to have played an important role in this local extinction. A study published earlier this year suggested a sudden cold snap about 24,000 years ago was implicated in the Neanderthals' disappearance from their Iberian refuge.
In the new research, an international team turned to a site at Gibraltar called Gorham's Cave.
Radiocarbon dating of material form that cave has suggested the Neanderthals may have died out between 32,000 to 24,000 years ago.
Costa del Neanderthal
The researchers mapped three radiocarbon dates spanning this period - 32,000, 28,000 and 24,000 years ago - on to a well-dated palaeoclimate archive based on deep-sea cores drilled in Venezuela. The archive relates records of past climate to radiocarbon dates.
They discovered that 32,000 and 28,000 radiocarbon years ago, Europe was experiencing conditions similar to the general climatic instability of the previous glacial period - conditions the Neanderthals had already proven able to survive.
Professor Katerina Harvati, an author of the paper and a palaeoanthroplogist from the Max Planck Institute for Evolutionary Biology, Germany, said: "The more controversial date of circa 24,000 years ago, places the last Neanderthals just before a major climate shift that would have been characterised by a large expansion of ice sheets and the onset of cold conditions in northern Europe.
"But Gibraltar's climate would have remained relatively unaffected, perhaps as a result of warm water from the sub-tropical Atlantic entering the western Mediterranean."
Speaking at the BA festival in York, she concluded: "Our findings suggest that there was not a single abrupt climatic event that caused the extinction of the Neanderthals."
Professor Harvati added: "This eliminates catastrophic climate change as a cause for extinction, but this leaves a whole range of other possibilities."
Professor Clive Finlayson is director of the Gibraltar Museum and co-authored the paper proposing a link between the sudden cold snap and the extinction of Neanderthals in southern Iberia.
Although he said he welcomed the interest in Gorham's Cave, he also saw several problems with the conclusions of the latest study. Firstly, he said, it was "strange" to try to link climatic events in the Caribbean with ones in Europe.
"I think they've missed the point," he told the BBC News website, "those dates, 32,000, 28,000 and 24,000 years ago, are occupation dates. They're dates when there are enough Neanderthals around for them to be picked up in the archaeological record.
"Whichever of those three dates you choose, populations would have gone extinct after that. They are trying to match this event with a time when Neanderthals were still around and are doing alright - within the limits of being a late population.
"This climatic event, which they say is 3,000 years later than our occupation date at 24,000 years ago, coincides perfectly with a period of no Neanderthals and no modern people in Gorham's Cave. That was music to my ears."
In their Nature paper, Professor Harvati and her colleagues contend that if the Neanderthals did die out at the later date of 24,000 years ago, climate changes in the north might have pushed modern humans further south into the Neanderthals' territory - forcing them into competition for scarce resources.
But Professor Finlayson explained there was no evidence for a southward human migration at this time. He said there was only one site in southern Spain with evidence for modern human occupation at the same time as Neanderthals were in the region - and even that one was disputed.
The next evidence for modern humans in southern Iberia comes several thousand years after the last evidence for Neanderthals at Gorham's Cave.