The two, aged 13 and 15, are the sons of Pele’s daughter Sandra Regina, who died in 2006.
They are seeking support payment of $6,000 for each to cover health insurance and education as well compensation of an unspecified amount.
The daily quoted their lawyer, Claudio Forssell, as saying that the teenagers “were abandoned intellectually, morally and materially” by their grandfather.
“Pele always rejected them,” according to the lawyer who said the teenagers had not met with their grandfather since 2011.
Pending a final ruling scheduled for next month, judges ordered Pele to pay each grandchild $760.
Born Edson Arantes do Nascimento and nicknamed O Rei (the king), Pele, now 72, is widely considered the greatest player of all time having helped Brazil win World Cup titles in 1958, 1962 and 1970.