A senior aide to Palestinian President Mahmoud Abbas gave no indication the Authority, which exercises limited self-rule in the occupied West Bank, would issue any call for calm, and blamed Israel for the spike in unrest.
The death in an Israeli jail of a Palestinian detainee on Saturday and an on-going hunger strike by four inmates have fuelled tensions in the West Bank, where stone-throwing protesters clashed again with Israeli soldiers on Sunday.
Some 3,000 prisoners held a one-day fast on Sunday after the detainee's death, which Israel said was caused by a heart attack, an explanation challenged by Palestinian officials.
"Israel has conveyed to the Palestinian Authority an unequivocal demand to calm the territory," an Israeli government official said, adding the message was delivered by one of Prime Minister Benjamin Netanyahu's top aides.
As an apparent incentive to Palestinian leaders to intervene, Israel pledged to proceed with this month's transfer to the Authority of around $100 million in tax revenues that it collects on its behalf.
In the latest clashes, hundreds of Palestinian protesters, in several towns and villages in the West Bank, hurled stones at Israeli soldiers, who responded with tear gas and stun grenades.
There were no reports of serious injuries in the confrontations, after a wave of violent protests last week in solidarity with the four hunger-striking prisoners.
Some 4,700 Palestinians are in Israeli jails, many of them convicted of anti-Israeli attacks and others detained without trial. Palestinians see them as heroes in a statehood struggle, and the death of any of the hunger-strikers would likely trigger widespread violence.
Abbas said in an Israeli television interview three months ago he would not allow a third armed Intifada to break out and that Palestinians would pursue their cause peacefully.
Amos Gilad, a senior Israeli Defence Ministry official, questioned whether the protests were just a tactical move by the Palestinians to draw international attention before Obama's visit to Israel, the West Bank and Jordan.
But he added, in an Israel Radio interview: "Things can get out of control."
Netanyahu has said Iran's nuclear programme would top the agenda of his meetings with Obama, but that the talks also would deal with Israeli-Palestinian peace efforts stalled since 2010.
Israel said it would carry out an autopsy of the body of Arafat Jaradat, the 30-year-old prisoner who died on Saturday. Israel's Prisons Authority said he had not been on a hunger strike and had been examined by an Israeli doctor during an interrogation on Thursday.
The first Palestinian uprising began in 1987 and ended in 1993, when the Oslo interim peace accords were signed.
The second Intifada broke out in 2000 after the failure of talks on a final peace settlement. Over the following seven years, more than 1,000 Israelis died, half of them in suicide attacks mostly against civilians, and more than 4,500 Palestinians were killed by Israeli forces.
Additional reporting by Ali Sawafta, Nidal al-Mughrabi, Noah Browning and Ari Rabinovitch; Editing by Rosalind Russell