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The newspaper cited unidentified investigative sources as saying the attempted call from co-pilot Fariq Abdul Hamid's phone was picked up by a cellphone tower as the plane was about 200 nautical miles northwest of the west coast state of Penang. That was around where military radar made its last sighting of the missing jet at 2:15 a.m. local time on March 8.
"The telco's (telecommunications company's) tower established the call that he was trying to make. On why the call was cut off, it was likely because the aircraft was fast moving away from the tower and had not come under the coverage of the next one," the New Straits Times cited a source as saying.
Government officials could not immediately be reached for comment on the report. The New Straits Times quoted acting Transport Minister Hishammuddin Hussein as saying that the report needed to be verified.
But he appeared to cast doubt on the report by saying: "If this did happen, we would have known about it earlier."
The New Straits Times cited separate investigative sources as saying that a signal had been picked up from Fariq's cellphone, but that it could have resulted from the device being switched on rather than being used to make a call.
Malaysia is focusing its criminal investigation on the cabin crew and the pilots of the plane -- 53-year-old captain Zaharie Ahmad Shah and 27-year old Fariq -- after clearing all 227 passengers of any involvement, police have said.
Investigators believe that someone with detailed knowledge of both the Boeing 777-200ER and commercial aviation navigation switched off the plane's communications systems before diverting it thousands of miles off its scheduled course.
The search for the missing jetliner in the southern Indian ocean resumed on Saturday, amid fears that batteries powering signals from the black box recorder on board may have died.