The world has already warmed by nearly 1C since pre-industrial times, and there are concerns that the ice sheet could reach a tipping point at around 1.5C to 2C of warming, lead author Luke Trusel said.
Climate change has forced the melting of Greenland's mile-thick ice sheet into "overdrive", threatening to boost global sea levels to risky levels.
The increased melting began around the same time humans started altering the atmosphere in the mid-1800s, said Trusel, lead author of a study of the meltwater runoff that was published Wednesday in the journal Nature.
"The melting and sea level rise we've observed already will be dwarfed by what may be expected in the future as climate continues to warm", he said.
Ice sheet melting began to increase soon after the mid-1800s.
Ice loss from Greenland, including runoff from melted snow and ice on the top of the ice sheet, is contributing to sea level rises.
The researchers warned that their findings also showed that it would only take a little additional warming to cause ice sheet melting to spike and sea levels to rise.
To determine how the Greenland ice had melted, researchers used a drill to extract ice cores.
To determine how intensely Greenland ice has melted in past centuries, the research team used a drill the size of a traffic light pole to extract ice cores from the ice sheet itself and an adjacent coastal ice cap, at sites more than 6,000 feet above sea level.
"We are seeing levels of Greenland ice melt and runoff that are already unprecedented over recent centuries (and likely millennia) in direct response to warming global temperatures since the pre-Industrial era", Sarah Das, co-author of the report and scientist at the USA -based Woods Hole Oceanographic Institution said in a statement.
"From a historical perspective, today's melt rates are off the charts and this study provides the evidence to prove it", said Sarah Das, a glaciologist at Woods Hole Oceanographic Institution in MA and co-author of the study.
But at higher elevations the summer meltwater quickly refreezes from contact with the below-freezing snowpack sitting underneath, preventing it from escaping the ice sheet in the form of runoff.
From these numbers, the researchers estimated that ice sheet-wide levels of meltwater runoff have jumped 50 per cent in the past 20 years compared with pre-industrial times.
Dr Trusel, from Rowan University's School of Earth and Environment in New Jersey, US, said Greenland would melt more and more for every degree of warming.
Dr Trusel said: "To be able to answer what might happen to Greenland next, we need to understand how Greenland has already responded to climate change".
"What our ice cores show is that Greenland is now at a state where it's much more sensitive to further increases in temperature than it was even 50 years ago".