"Whether they like it or not, our state is already established," Arafat told reporters on his return from a visit to North Africa and Europe, apparently referring to leaders of Israel's right-wing government.
Earlier, Israeli Prime Minister Benjamin Netanyahu proclaimed victory for thwarting Arafat's long-standing pledge to declare statehood on May 4.
In the West Bank, Israeli troops firing rubber-coated bullets shot and wounded at least 17 Palestinians protesting at the delay in the proclamation, witnesses said.
The Palestine Liberation Organization, under intense international pressure, decided last week not to declare statehood.
The move was a retreat by Arafat, who heads the Palestinian Authority that administers interim self-rule in parts of the West Bank and Gaza. Arafat had pledged for months that May 4 was a "sacred date" for Palestinians.
"Netanyahu should not lie to himself, thinking that he has won," said Nabil Shaath, a senior Palestinian peace negotiator who accompanied Arafat on his trip abroad.
"Netanyahu knows very well that we have gained a lot on this day and that the world which stands beside us looks at him with suspicions and with doubts," Shaath said.
Fighting for re-election in a May 17 election, Netanyahu called Arafat a "wise man" for realizing the gravity of Israel's threat to annex parts of the West Bank and Gaza should the Palestinian leader move to declare a state.
This is a great achievement for the state of Israel and the government of Israel," Netanyahu, who is trailing behind opposition Labor party leader Ehud Barak in election polls, told reporters.
The United States has urged Israelis and Palestinians to return to the bargaining table after Israel's election to complete a final peace accord within a year.
In the West Bank town of Hebron, witnesses said hundreds of Palestinian protesters, some masked and brandishing automatic weapons, rained stones and petrol bombs on Israeli troops and blasted Arafat for failing to declare independence.
Israeli troops opened fire with rubber-coated metal bullets, wounding 14 Palestinians and an Israeli television cameraman, the witnesses said. Most suffered light wounds but a rubber bullet struck one man in the head.
Three Palestinians were slightly wounded during a protest in the West Bank town of Beituniya. Demonstrations in other parts of the West Bank and Gaza passed without serious incidents of violence.