Annan said he was "acutely conscious of the dangers of a further deterioration" and had spent the day in intensive talks with leaders in the region and other statesmen who have influence with the key parties to try to calm the situation.
Ten days of clashes have claimed the lives of 80 people and injured over 1,900 people, mainly Palestinians.
Noting that violence between the Palestinians and Israelis had spread to the Israeli-Lebanese border and the Chebaa farms area of the Golan Heights, Annan appealed to the parties "to show the utmost restraint and rein in their forces and supporters."
This will give "the ongoing efforts to restore the peace process the best chance of success," Annan said in a statement.
The secretary-general also urged Israelis and Palestinians "to maintain the inviolability of religious sites of importance to other faiths."
Israel's U.N. Ambassador Yehuda Lancry sent a letter to the council Saturday afternoon saying Israel holds the governments of Lebanon and Syria "fully and directly responsible" for kidnapping the three Israeli soldiers and attacking and shelling Lebanon's border with Israel.
"Israel calls on the Security Council to act urgently ... to secure the immediate and safe return of the Israeli hostages and the cessation of all aggressive activity from Lebanese territory against Israel," he said.
Lancry said the incidents on the border marked "a drastic and dangerous deterioration in the already sensitive and tense situation in the Middle East." The Security Council statement dropped an earlier draft's reference to the kidnapping of the three Israeli soldiers and the deaths of three Palestinians. With the U.S. abstaining, the council on Saturday night also passed a resolution condemning "the excessive use of force against Palestinians" and calling for an immediate cessation of violence.
On Sunday, the leader of Hadassah, the women's Zionist organization, denounced the Security Council's approval of the resolution.
With the vote the Security Council "has proven itself to be one-sided with regard to the Middle East," said Bonnie Lipton, national president of Hadassah.
"Included in the resolution should have been condemnation of: the kidnapping of three Israeli soldiers from within U.N.-recognized Israeli territories and the destruction of Joseph's tomb, a Jewish holy site, both of which have taken place in the last 48 hours; and the denial of the Jewish historical connection to the Temple Mount, Judaism's holiest site," Lipton wrote.
She said the United States' decision to abstain from voting "allows yet another United Nations Security Council resolution against Israel to be promulgated without regard to the facts on the ground."
Religious groups such as Churches for Middle East Peace and the American Muslim Council also condemned Israeli troops' use of forceagainst Palestinians and civilians. The Evangelical Lutheran Church in America (ELCA) denounced the Israel troops' "disregard for humanitarian organizations such as the Augusta Victoria Hospital."
According to a hospital news release distributed by the ELCA, Israeli troops entered the grounds of the hospital Sept. 29 and have opened fired on Palestinians outside the hospital's property.
Israeli forces have been preventing patients and wounded people from entering the hospital, according to the church's presiding bishop, the Rev. H. George Anderson.
"We ... demand that Israeli troops not use the perimeter of the hospital nor the property of the Lutheran World Federation for military activity," Anderson said in a statement. "Their presence is provocative and may lead to additional casualties."