Mr. Shtayyeh, 61, was a top economic-development official and an occasional participant in peace talks with the Israelis before being appointed to the No. 2 job in the Palestinian Authority in March. His boss, President Mahmoud Abbas, is in his 80s and in poor health. Since then Mr. Shtayyeh has set about trying to increase public confidence in the authority, while also showing a common touch, as if he hoped to be a candidate to succeed Mr. Abbas.

But he starts his job facing an immediate financial crisis.

In February, under a 2018 law modeled on the American Taylor Force Act, Israel began deducting about $138 million in what it calls “pay-to-slay money” from the roughly $2.5 billion a year in taxes and tariffs that it collects for and transfers to the Palestinians.

The deduction is equal to Israel’s tally of the financial support that the authority provided last year to Palestinians in Israeli prisons for attacking Israelis, to their families, and to the families of those “martyred” or killed long ago in uprisings against Israel, including suicide bombers.

Israel and Western countries see those payments, which began in the 1960s, as incentivizing terrorism. But the Palestinians see them as a vital form of welfare that rewards the sacrifices made by freedom fighters and their families, and say that many prisoners had no part in violence and did not receive fair trials. Unilateral deductions by Israel, they say, violate the agreements under which Israel collects revenue for the Palestinians.

Mr. Abbas responded by refusing to accept any revenue transferred from Israel, effectively giving up more than half the authority’s income and setting it on a kamikaze course if Israel does not repeal or suspend its new law.