Scientists said the “unprecedented” melting took place over a larger area than has been detected in three decades of satellite observation.
Melting even occurred at Greenland’s coldest and highest place, Summit station.
The thawed ice area jumped from 40% of the ice sheet to 97% in just four days from 8 July.
Although about half of Greenland’s ice sheet normally sees surface melting over the summer months, the speed and scale of this year’s thaw surprised scientists, who described the phenomenon as “extraordinary”.
Nasa said that nearly the entire ice cover of Greenland, from its thin, low-lying coastal edges to its centre, which is 3km (two miles) thick, experienced some degree of melting at its surface.
Until now, the most extensive melting seen by satellites in the past three decades was about 55% of the area.
According to ice core records, such pronounced melting at Summit station and across the ice sheet has not occurred since 1889.
“When we see melt in places that we haven’t seen before, at least in a long period of time, it makes you sit up and ask what’s happening,” Nasa chief scientist Waleed Abdalati said.
“It’s a big signal, the meaning of which we’re going to sort out for years to come.”
Watch this space
He said that, because this Greenland-wide melting has happened before – in 1889 – scientists are not yet able to determine whether this is a natural but rare event, or if it has been sparked by man-made climate change.
“Ice cores from Summit show that melting events of this type occur about once every 150 years on average. With the last one happening in 1889, this event is right on time,” said Lora Koenig, a glaciologist from Nasa’s Goddard Space Flight Center in Maryland and a member of the research team analysing the satellite data.
“But if we continue to observe melting events like this in upcoming years, it will be worrisome.”
Prof Eric Wolff, from the British Antarctic Survey (Bas) told BBC News: “There have clearly been some very warm days in Greenland this month. As a result, the surface snow has melted across the whole ice sheet.
“This is confirmed by some of my international colleagues who are on the ground at the NEEM ice core drilling site in north Greenland – they are reporting several days with temperatures above zero, and ice layers forming in the snow.
“While this is very unusual, as always we cannot attribute any individual extreme event to climate change: We will have to wait and see if more such events occur in the next few years to understand its significance for both the climate and the health of the ice sheet.”
Dr Poul Christoffersen, a glaciologist and engineer at the Scott Polar Institute in Cambridge, told BBC News: “The melting seen in the satellite data is unprecedented, as it extends all the way across the ice sheet including the summit, which is located 3,200 m above sea level. Melting is usually limited to less than 2000m elevation.”
The news comes just days after Nasa satellite imagery revealed that a massive iceberg, twice the size of Manhattan, had broken off the Petermann Glacier in Greenland.
“The observation [from Greenland] is in my view much more important than the recently reported break up of a large iceberg from Petermann Glacier,” Dr Christofferson added.
Nasa’s Tom Wagner said: “This event, combined with other natural but uncommon phenomena, such as the large calving event last week on Petermann Glacier, are part of a complex story.”
Scientists said they believed that much of Greenland’s ice was already freezing again.