In a rare display of non-hostile rhetoric, the Palestinian Authority President, Mr Yasser Arafat, declared a unilateral intifada ceasefire yesterday, and the Israeli Prime Minister, Mr Ariel Sharon, said he was giving Mr Arafat "a chance".
On the ground, however, it was hard to discern much in the way of moderation.
In pre-dawn fighting in Gaza's Rafah refugee camp, Israeli troops shot dead a Palestinian man said by eyewitnesses to have been mentally handicapped and to have wandered into the battle zone; two more Palestinians died of injuries sustained in fighting in Gaza and Jericho late last week; a 12-year-old Palestinian boy, one of several throwing stones at soldiers near Gaza's Netzarim settlement, was shot in the head, eyewitnesses said; and several Palestinian gunmen and at least one Israeli soldier were hurt in the course of a two-hour gun-battle outside Ramallah.
In both the Rafah and Ramallah clashes, each side accused the other of initiating the fighting.
Against that improbable background, Mr Arafat published a letter to the Israeli people, timed to coincide with today's Jewish New Year, in which he said he had "issued strict instructions for a total commitment to the ceasefire" to all Palestinian groups and to his own PA security apparatus.
"I hope the Israeli government will respond to this peace appeal," he added, "and will take the decision to cease fire and will stop its escalatory military measures against our people."
The letter came a day after Mr Sharon had urged Mr Arafat to call a truce; the Prime Minister had promised that, if this request was met, he would immediately do the same - including halting "initiated operations" to eliminate alleged intifada orchestrators.
Mr Sharon did not respond immediately to Mr Arafat's letter, but in a New Year's interview recorded earlier in the day, he had said he was "still giving Arafat a chance" to end the violence and reiterated that he would sanction formal ceasefire talks between Mr Arafat and the Israeli Foreign Minister, Mr Shimon Peres, if there were 48 hours of quiet.
The Prime Minister insisted that he had a peace plan, which he would unveil once calm was achieved.
Nevertheless, he made clear that he would "never, not once, allow a situation in which Israel is attacked, and I then duck and lower my head in mourning ... If they attack, I hit back," he said.
Mr Sharon also used the interview, coming almost exactly a year after the intifada erupted, to defend his controversial visit to the Temple Mount, as the then-opposition leader, last September 28th - the day before the violence broke out.
He noted that he had not entered the mosques on the site, although he had done so in the past. He also said he felt he had behaved with respect.
"It is the right of every Jew," he added, "to go up to the Temple Mount" - a compound sacred to Jews as the site of the Temple and to Muslims as the site of the Prophet Muhammad's ascent to heaven.
Palestinian leaders have said that Mr Sharon's visit, secured by a large contingent of police and soldiers, constituted a deliberate provocation, triggering the intifada.