Israel has contended the council did not recognize Israel and had not outlawed terrorism.
Arafat, chairman of the Palestine Liberation Organization, has had two days of talks in the Swedish capital with a delegation of five U.S. Jewish intellectuals.
"The PNC accepted two states, a Palestinian state and a Jewish state, Israel. Is that clear enough?" Arafat told the news conference.
He added that the uprising in the Israeli-occupied territories on the West Bank and in the Gaza Strip would continue until a Palestinian state was established.
Swedish Foreign Minister Sten Andersson said the declaration was intended to elaborate on the PLO's acceptance last month of the two U.N. resolutions, which implicitly recognize Israel.
Andersson said that according to the declaration, the PLO parliament-in- exile last month "established the independent state of Palestine and accepted the existence of Israel as a state in the region."
Arafat said he had asked Andersson to convey the spirit of the declaration issued by himself and the Jewish delegation to U.S. Secretary of State George Shultz "despite his previous attitude in depriving me of a visa."
U.S. immigration authorities turned down Arafat's application for a visa to address a debate on the Middle East at the United Nations in New York, saying he supported terrorism. The refusal caused the world body to move the debate to Geneva.
Arafat said he wanted to discuss the future of the region in a special U.N.-sponsored international conference.
The statement issued by Arafat and the Jewish delegation said the PLO ''declared its rejection and condemnation of terrorism in all its forms."
The Israeli government and prominent Jewish groups in the United States dismissed the meetings and condemned the talks as a publicity stunt for Arafat.
The Jewish delegates to the talks in Sweden belong to a research body called the International Center for Peace in the Middle East.
Rita Hauser, head of the delegation, said she welcomed the decision of the PLO to accept the right of Israel to exist.
"There can be no question that this statement is a clear recognition of Israel. The PLO has accepted the existence of Israel as a state in the region," Hauser said.
She called on the U.S. administration to open direct dialogue with the PLO and said she was sure most U.S. Jews would support the move.
Hauser said the statement was being communicated to Shultz, who had been told before the Jewish delegation left the United States that the talks with Arafat were to take place.
Hauser said PNC resolutions had been seen by many as ambiguous regarding the acceptance of Israel and renouncing terrorism.
"But that is exactly what they meant, that is exactly what they now have said," she stated.