Greenland is currently losing about 100 billion tonnes of ice a year.
Much of the ice is being lost from southeast Greenland
US space agency (Nasa) scientists have undertaken a new assessment of the rate of melting occurring on the great ice sheet that covers the region.
Their data comes from satellites that detect changes in mass by monitoring tiny fluctuations in the pull of gravity as they fly over the Earth.
Scott Luthcke, from the Goddard Space Flight Center, and colleagues report their study in the journal Science.
The rate of ice loss observed using the Grace (Gravity Recovery and Climate Experiment) spacecraft is much lower than other recent research using the same data has suggested.
The Luthcke team says it has used a different analysis technique - one that enabled the group to determine the behaviour of individual drainage systems instead of looking at the ice sheet as a whole.
The results indicate that Greenland lost about 100 billion metric tonnes (or gigatonnes, Gt) of ice per year from 2003 to 2005. Other estimates for the same period have been close to 240 Gt of ice.
Both figures, however, contrast with findings showing that the ice sheet's overall volume was roughly constant during the 1990s.
The Science authors also found, as others have, that the ice sheet is thinning at the margins while growing a little in the interior. This fits with climate models of a warmer world which expect increased melting at the edges of Greenland and increased snowfall on more central, higher locations.
According to this study, though, Greenland is now losing 20% more mass than it receives from new snowfall each year.
"This is a very large change in a very short time," said co-author Jay Zwally.
"In the 1990s, the ice sheet was growing inland and shrinking significantly at the edges, which is what climate models predicted as a result of global warming. Now the processes of mass loss are clearly beginning to dominate the inland growth, and we are only in the early stages of the climate warming predicted for this century."
The contribution to global sea-level rise of the ice loss observed in this study is about 0.3mm per year.
Commenting on the Grace research, Anny Cazenave, from the Observatoire Midi-Pyrenees, France, said scientists still had much work to do, to pull all their observations together and build a full picture of ice mass trends.
"Because of these contrasting behaviours - mass loss in coastal regions and mass gain in elevated central regions - ice-sheet mass loss exceeds mass gain only slightly," the Toulouse-based researcher said.
"Thus according to the recent mass-balance estimates, the ice sheets presently contribute little to sea-level rise. However, great uncertainty remains, mainly because of incomplete coverage by remote-sensing surveys, spatial and temporal undersampling, measurement errors, and perturbation from unrelated signals."