In Ramallah’s central square, rapt crowds watched Mr. Abbas deliver his address on large television screens, bursting into cheers as he held up sheets of paper and announced that it was a copy of the letter he had just submitted to the United Nations Secretary General requesting statehood recognition.
Many in the crowd, which streamed in from surround streets in the hours before the address, which began just after nightfall, carrying candles and placards bearing the likeness of the Palestinian president, who has slowly emerged from the shadow of his predecessor, Yasir Arafat, during his bid at the United Nations.
Anass Amarneh, 25, had come from the northern West Bank town of Jenin to the central square here, recently renamed Martyr Yasir Arafat Square. “We are proud; this is an important achievement,” he said, holding a placard and a candle. “Abu Mazen is trying to achieve our goals and our dreams. If he fails, at least he had the honor of having tried,” he said, using the popular name for Mr. Abbas.
A festive feeling permeated the crowd and after the speech ended the chants began in earnest, with many repeating the old Palestinian refrain: “In blood and spirit, we will redeem you, oh Palestine.”
At least one Palestinian was killed in a pre-speech clash with Israeli settlers and security forces at Kalandia, the often-tense crossing point between Ramallah and Jerusalem. The violence continued throughout the day and into the night, but did not escalate beyond a small number of people.
The Israeli military has heavily increased its presence around the West Bank, worried that the Palestinian move toward international recognition of its statehood might inspire large-scale marches or violence against some of the 330,000 Israeli settlers in the West Bank. They were equally concerned that radical settlers could promote confrontations.
A police spokesman said there were 22,000 Israeli police deployed in the West Bank.
At Kalandia, Israeli troops used tear gas against several dozen stone throwers. Near the village of Qusra, a dozen settlers from a nearby outpost arrived to pray, an act viewed as a provocation by the villagers. Several thousand Palestinians marched toward them, some with Palestinian flags, and Israeli troops intervened. There were a few injuries and a Palestinian protester was among the dead. The Israeli military said it was investigating how that had happened.
Israel barred access to men under age 50 to Jerusalem’s Al Aqsa Mosque, Islam’s third holiest site, afraid of unrest. The prayer sessions ended without incident.
In the village of Nabi Saleh, where there are weekly Friday demonstrations against Israeli occupation, a large chair painted in the blue of the United Nations was carried in a procession, a symbol of the aspiration for Palestine to be declared the organization’s 194th member. Israeli flags and posters of President Obama were also burned — Mr. Obama’s Wednesday speech at the General Assembly angered Palestinians for its pro-Israel content.
In Gaza, ruled by the Islamist group Hamas, rivals to Mr. Abbas’s Fatah party, Prime Minister Ismail Haniya told reporters after Friday Prayer that the United Nations membership bid was a mistake because “the Palestinian people do not beg for a state.” He said the only hope was for a Palestinian state to be “snatched from the Zionist occupation, not the United Nations.”
He added, “As Palestinians, we want a state. But this state must enjoy full sovereignty and must not be at the expense of the Palestinian rights and principles, mainly the right of return to our land that Israel has occupied in 1948.”
Mr. Haniya also called on Mr. Abbas to start a dialogue with Hamas if the United Nations effort fails.
“Given the American oppression and European dodge, we tell Abbas to come back to the Palestinian people and launch a strategic national dialogue,” he said. “This strategy must be based on maintaining the national principles, resistance, bolstering the Palestinian people and increasing diplomatic and political work with our Arab brothers.”
Isabel Kershner reported from Ramallah and Ethan Bronner from Jerusalem. Reporting was contributed by Rina Castelnuovo in Qusra, West Bank, and Fares Akram in Gaza.
The Last Days 
Ban Ki-Moon's decision to submit the Palestinian bid to the Security Council immediately instead of hanging on to it for a while is somewhat surprising. It also suggests that hopes for a compromise look more slender.