Although the president is a ceremonial post, Herzog convened 100 heads of authorities for an emergency meeting on how to come up with a solution on proposals that have split the country and led to nationwide protests, some of which have turned into battles with police.
"We are closer than ever to the possibility of an agreed outline. There are agreements behind the scenes on most things," Herzog said in a statement, without giving details.
He said it would now depend on leaders of the ruling coalition and opposition to "put the country and the citizens above everything else" and implement it, adding that his plan works to placate both sides.
The judicial overhaul plan, which has already received initial parliamentry approval, would give the government greater sway on selecting judges and limit the power of the Supreme Court to strike down legislation.
Critics of the planned law changes say Prime Minister Benjamin Netanyahu - on trial on graft charges that he denies - is pursuing steps that will hurt Israel's democratic checks and balances, enable corruption and bring diplomatic isolation.
Proponents say the changes are needed to curb what they deem an activist judiciary that interferes in politics.
Opposition leader Yair Lapid has called for compromise talks and a freeze of the legislation for 60 days but Netanyahu said he would only agree to negotiations without preconditions.
Since the proposals were introduced in late January, the shekel has slumped against the dollar, alarming investors wary that Israel might be joining the growing list of emerging markets taking a more authoritarian stance to decision making.
By last week, its losses reached nearly 10% against the U.S. currency in one month to a three-year low.
But analysts said optimism over a compromise sent the shekel up 2% on Monday to 3.59 per dollar - its strongest level since Feb. 21. Similarly, Tel Aviv share indexes and government bond prices were also up close to 2%.
(Reporting by Steven Scheer; Editing by Angus MacSwan)
By Steven Scheer
