The plant had been idle since Sunday amid a crisis triggered by an Israeli fuel blockade of Gaza announced on Friday in response to rocket attacks from militants in the Hamas-controlled territory.
"We processed the delivered diesel fuel and put back into operation one [of the four] turbines of the plant. We will start the second and increase output to 70% of the norm by night," the spokesman said.
Palestinian Authority President Mahmoud Abbas said a temporary lifting of the Gaza blockade was "insufficient".
A Gaza Health Ministry official said the blackout had caused the death of five patients in hospitals during the early hours of Monday.
International criticism of the blockade has been widespread, with UN officials saying that Israel was imposing "collective punishment" on Gaza's 1.5 million people.
Israeli Prime Minister Ehud Olmert had earlier stated that life would not be "pleasant or comfortable" for those in Gaza if rocket attacks on Israel continued.
Israel accused Hamas of 'fabricating' power cuts, however, pointing out that the Gaza plant meets one fourth of Gaza's energy needs, with the rest of its electricity coming from Israel and Egypt. Israel said it had continued with electricity supplies to Gaza, despite the blockade.
The Israeli fuel delivery on Tuesday morning has been announced as a one-off measure after a drop in the number of Palestinian rocket attacks against Israel.
The Jerusalem Post earlier said that Gaza would receive 2.2 million liters of diesel fuel for its power station.
Hospitals and medical institutes were also to receive 500,000 liters of fuel for their generators, and trucks were to deliver medicine and food to the impoverished enclave.
