Three Grad rockets were fired at Israeli positions in occupied Palestine, the "Sinai Province" group said in a statement on Twitter, Reuters reported.
An Israeli military spokesman said earlier that two rockets fired from Sinai exploded inside Israel without causing casualties.
The group said the rocket fire was in retaliation for alleged Israeli support for Egypt's armed forces on Wednesday when the group attacked army checkpoints in northern Sinai.
Egypt's military deployed F-16 warplanes to bombard ISIL who battled troops after launching their surprise dawn attack.
Dozens were killed in what was ISIL's boldest attack yet in the strife-torn Sinai.