TEL AVIV (Reuters) -Tens of thousands of flag-waving Israelis renewed their protests nationwide after sundown on Saturday, capping a week of turmoil in which Prime Minister Benjamin Netanyahu pushed through a highly contested law that limited some Supreme Court power.

From a remote intersection among the lush hills of the northern Galilee to the avenues criss-crossing the financial hub of Tel Aviv, protesters beating drums and blaring horns took to the streets on a hot evening at the end of Sabbath.

The judicial overhaul pursued by Netanyahu and his right-wing government, the first part of which passed on Monday, has sparked an unprecedented crisis and opened up a deep social divide. The protests are in their 30th week.

The government's plan has shaken the commitment to call-up duty of some army reservists while drawing stern warnings of economic fallout from ratings agencies.

"We all don't see any future if this will keep on going," said Yariv Shavit, 53, an engineer in Israel's high-tech sector who gathered with other protesters carrying a flower and a flag. "We are not united. We lost our unity."

Political watchdog groups have appealed to the Supreme Court to strike down the new law, which removes the high court's authority to void what it deems "unreasonable" decisions by government and ministers. The court said it would hear arguments in September, setting the scene for a constitutional showdown.

Netanyahu has tried to minimize the impact of the new law, ratified after days of rowdy debate in parliament in a vote boycotted by the opposition.

Critics say he is threatening Israel's democratic principles and independence of the courts, possibly with an eye to a corruption case he himself is facing. Netanyahu denies that, and also denies the charges against him.

The Knesset, Israel's parliament, adjourns for recess on Saturday, so it could be weeks before Netanyahu's future strategy becomes clear. Together with ultra-Orthodox and nationalist partners he controls 64 of 120 seats.

But there appear to be signs of unease and even regret within Netanyahu's own Likud party.

One Likud lawmaker admitted during an interview to "falling asleep on watch" and another wrote on Facebook that going forward he would only support changes reached in "a broad national agreement".

(Reporting by Rami Amichay and Ari RabinovitchEditing by Frances Kerry and Giles Elgood)