The research is described in the magazine Science by Bill Krabill, project scientist at the Nasa Goddard Space Flight Center's Wallops flight facility at Wallops Island in Virginia.
Nasa scientists say the ice around the coast of Greenland is still thinning fast, by more than one metre (three feet) annually.
At a conservative estimate, they say, the entire ice sheet is undergoing a net loss of about 51 cubic kilometres of ice each year.
This is enough to raise global sea level by 0.012 cm (0.005 inches) annually, about 7% of the observed rise.
But while most coastal areas are now experiencing significant thinning, some inland parts of the sheet show slight ice thickening.
Nasa has been surveying the Greenland ice sheet for almost seven years. In 1993 and 1994, researchers used an airborne laser altimeter and precision global positioning satellite receivers, and surveyed the same areas again in 1998 and 1999.
Several factors
Now, for the first time, parts of the sheet have been mapped accurately enough to detect significant changes in elevation.
The research is described in the magazine Science by Bill Krabill, project scientist at the Nasa Goddard Space Flight Center's Wallops flight facility at Wallops Island in Virginia.
He said: "This amount of sea level rise does not threaten coastal regions, but these results provide evidence that the margins of the ice sheet are in a process of change.
"The thinning cannot be accounted for by increased melting alone. It appears that ice must be flowing more quickly into the sea through glaciers.
"Why the ice margins are thinning so rapidly warrants additional study. It may indicate that the coastal margins of ice sheets are capable of responding more rapidly than we thought to external changes, such as a warming climate."
Models vindicated
In March 1999, Nasa reported that the Greenland ice sheet was thinning by up to a metre a year. They said then they thought a more probable explanation than global warming was a process in which water filtered down to the bedrock, making the ice likelier to slip off.
Dr David Viner, of the Climatic Research Unit at the University of East Anglia, UK, told BBC News Online: "These latest findings are totally in line with what the Intergovernmental Panel on Climate Change models have been predicting.
"But while the observations back up the modelling results, the contribution to sea level rise is very modest.
"It is about 4% of what we expect over the course of this century - somewhere between four and 10 cm a decade.
"What may prove a more important consequence than the rise in sea level is the reduction in albedo, the reflectivity of the ice.
"And if more cold fresh water is entering the north Atlantic, that could affect ocean circulation."
Dr Ghassem Asrar, associate administrator for Nasa's Office of Earth Science, said: "For the first time, we are seeing evidence that one of the two great ice bodies on the Earth (the other is the Antarctic ice sheet) is contributing, in a modest fashion, to observed sea level rise.
"Nasa's ICESat spacecraft, which is scheduled for launch in 2001, will allow us to make similar measurements routinely and keep an eye on both Antarctica and Greenland."