The findings of the study, which could lead to higher estimates of expected sea level rise in the future, appears in the latest edition of the journal 'Nature Climate Change'.
The study focuses on ice loss due to a retreat of an "outlet glacier" connected to a long "river" of ice, or the "ice stream", that drains ice from the interior of the ice sheet.
This ice stream, called the Zachariae ice stream, has retreated about 20 km over the past decade, the study found.
That's bad news. For, in comparison, one of the fastest-moving glaciers, the Jakobshavn in southwest Greenland, has retreated just 35 km over the last 150 years.
Ice streams drain ice basins, the same way rivers drain water basins.
Zachariae is the largest ice stream in a drainage basin that covers 16 percent of the Greenland ice sheet -- an area twice as large as the one drained by Jakobshavn.
The study represents the latest finding from GNET, short for "Greenland GPS Network", which measures ice loss by weighing the ice sheet as it presses down on the bedrock.
"Northeast Greenland is very cold. It used to be considered the last stable part of the Greenland ice sheet," GNET lead investigator Michael Bevis of Ohio State University has been quoted as saying.
"This study shows that ice loss in the northeast is now accelerating. So, now it seems that all of the margins of the Greenland ice sheet are unstable.
"This suggests a possible positive feedback mechanism whereby retreat of the outlet glacier, in part due to warming of the air and in part due to glacier dynamics, leads to increased dynamic loss of ice upstream. This suggests that Greenland's contribution to global sea level rise may be even higher in the future," said Bevis.
Study leader Shfaqat Abbas Khan, a senior researcher at the National Space Institute at the Technical University of Denmark, said the finding was a cause for concern.
"The fact that the mass loss of the Greenland Ice Sheet has generally increased over the last decades is well known," Khan said, "but the increasing contribution from the northeastern part of the ice sheet is new and very surprising."
Khan and his colleagues combined GNET data with ice thickness measurements taken by four different satellites.
They found that the northeast Greenland ice sheet lost about 10 billion tonnes of ice per year from April 2003 to April 2012.
In previous measurements and aerial photographs, the northeast Greenland ice sheet margin appeared to be stable for 25 years, till 2003.
Since then, a string of especially warm summers have triggered increased melting.
Increased ice flow in this region is particularly troubling, Khan said, because the northeast ice stream stretches more than 600 km into the center of the ice sheet where it connects with the heart of Greenland's ice reservoir.
The Greenland ice sheet is believed to be one of the largest contributors to sea level rise over the past 20 years, accounting for 0.5 millimeters of the current total of 3.2 millimeters of sea level rise per year.