The Muslim rebel group, which recently expressed allegiance to the Islamic State (IS), told a local radio station that Stefan Okonek, 71, will be killed at 5pm local time (09:00 GMT) unless their demands were met, Al Jazeera's Harry Fawcett, who is in Zamboanga City, reported.
The Abu Sayyaf group demanded a $5.6 million ransom in exchange for Okonek's release. The German doctor was seized together with his partner Henrite Dielen, also a German national, by the Abu Sayyaf rebels in April when their yacht broke down near the southern island of Palawan en route to Sabah in eastern Malaysia.
They are being held on Jolo island, a hotbed of separatist rebellion, in the south of the mainly Roman Catholic Philippines.
A video released on Wednesday showed Okonek being held in a hole in the ground, which he had been told would be his grave if ransom is not paid. The rebel group also demanded that Germany halt its support for US-led air strikes in Syria and Iraq against ISIS.
"They told me on Friday they will kill me," the doctor said in a radio interview monitored in Zamboanga City. "I'm here in a hole. It's a big hole, three metres (by) five metres. They told me this is my grave. They push me inside the hole. "I hope I will still get out from here ... but I have not seen anyone from the government to get into the situation that tries to get us out."
He said he was losing weight because there was not enough food and 10 gunmen were watching over him 24 hours a day. He was separated from the woman on Monday. This was the second time the German has spoken to commercial radio since last Friday's deadline passed.
The Abu Sayyaf also sent a video to a radio station late on Tuesday showing a group of men manhandling a handcuffed foreigner who was apparently the captured German man. The man in the video was saying that his handcuffs were too tight as armed men made him sit in front of black flag, which appeared to be the flag used by ISIS.
Earlier, the group called on Philippine Foreign Secretary Albert del Rosario to negotiate, offering hope for a possible solution.