Al Jazeera's Ayman Mohyeldin, reporting from Rafah, said: "They were not able to find them [the trapped men] on the Palestinian side ... they notified the Egyptians ... to immediately begin rescue efforts on their side of the border.
"We were told they were recovered unconscious ... they were immediately rushed to hospital in Egypt. Their fate is still unknown although officials have confirmed they are indeed alive."
Witnesses said the men had been able to communicate with rescuers for the first few days and were fed milk and water through a pipe that had been pushed through the sand.
Palestinians had been allowed to cross into the Egyptian side on Saturday to try to help with the rescue process.
Tunnels frequently bombed
Israel says the tunnels are used for smuggling weapons into Gaza and has frequently attacked them with bombs.
But Palestinians say the network of tunnels are a lifeline for them. They are used to smuggle in essential supplies, in short supply in the territory because of a blockade imposed by the Israelis.
"There are about 1000 tunnels that run under the route that we are standing at," our correspondent said.
"It is very soft terrain, very susceptible to collapse when vehicles pass over it and when Israel carries out air strikes as they have been doing almost daily since the end of the war [Israel’s 22-day offensive in Gaza].
Mohyeldin said the tunnels are operating "just to meet the demands of 1.5 million people who are denied access to basic food supplies and other essential items.
"Desperation is driving [Gazan] men into these very dangerous jobs.
"The three man rescued today are by far the minority. The vast majority of those ... who suffer entrapment underground do not make it out alive," he said.