The "unprecedented" melting is highest in three decades of satellite observation, NASA said in a statement.
Melting even occurred at Greenland's coldest and highest place, Summit station. The thawed ice area jumped from 40 per cent of the ice sheet to 97 per cent in just four days from Jul 8 to 12.
Although about half of Greenland's ice sheet normally melts over the summer months, the speed and scale of this year's melting surprised scientists, who described the phenomenon as "extraordinary".
Son Nghiem of NASA's Jet Propulsion Laboratory in Pasadena, California, was analyzing radar data from the Indian Space Research Organisation's (ISRO) Oceansat-2 satellite last week when he noticed that most of Greenland appeared to have undergone surface melting on July 12.
"This was so extraordinary that at first I questioned the result: was this real or was it due to a data error?" Nghiem said.
Nasa said that nearly the entire ice cover of Greenland, from its thin, low-lying coastal edges to its centre, which is 3 km thick, experienced some degree of melting at its surface.
"Satellite observations are helping us understand how events like these may relate to one another as well as to the broader climate system," said Tom Wagner, NASA's cryosphere program manager in Washington.
He said that, because this Greenland-wide melting has happened before, Nasa is not yet able to determine whether this is a natural but rare event, or if it has been sparked by man-made global warming.
Scientists said they believed that much of Greenland's ice was already freezing again.
Until now, the most extensive melting seen by satellites in the past three decades was about 55 per cent of the area.
Ice last melted at Summit station in 1889, ice core records show.
The news comes just days after Nasa satellite imagery revealed that a massive iceberg, twice the size of Manhattan, had broken off a glacier in Greenland.
