"This is a rather unique step which has never happened in the past," said German U.N. Ambassador Hanns Heinrich Schumacher.
But after a debate, the council unanimously agreed to defer the review until its next session in October and November at the latest. It could also take it up earlier.
Henczel said the compromise would set a precedent for "how to deal with all cases of non-cooperation" in the future.
All U.N. nations are required to submit to Human Rights Council review every four years. The council's spokesman, Rolando Gomez, said once previously Haiti did not appear for its review but provided a reason.
U.S. diplomats have said the council is too focused on Israel. Israel, meanwhile, said last year that it would stop cooperating with the council because of its plans for a fact-finding mission on Israeli settlements in the West Bank and East Jerusalem.