There was no immediate explanation as to why the Patriot - which has been spectacularly successful in destroying Iraqi Scuds aimed at Saudi Arabia - failed in this case.
The Israeli military offered few details about the attack, and it was not clear if more than one missile was fired at Tel Aviv last night.
It was the third Iraqi missile attack against Israel since the Persian Gulf war began last week, and by far the worst in terms of casualties and damage.
The attack immediately raised anew speculation that Israel might respond by attacking Iraq.
The United States has sought to keep Israel out of the Persian Gulf war, fearing problems with its Arab coalition partners. But some Arab states - Syria and Egypt - have said they would not pull out of the anti-Iraq coalition if Israel responded in a measured way to the Iraqi attacks.
In Washington, President Bush condemned Iraq for "this brutal act of terror against innocent victims" and called the attack "a continued example of Iraq's unprovoked aggression against (its) neighbors." Bush's statement also praised Israel's "remarkable restraint in the face of this aggression."
In New York, the Iraqi Ambassador to the United Nations, Abdul Amir al- Anbari, said his country attacked Israel because inflicting the "pain and suffering of war" on Israelis might lead them to reach a settlement with the Palestinians.
Tel Aviv residents had only a brief warning before the missile, armed with a conventional high-explosive warhead, exploded around 8:30 p.m. It instantly converted a quiet, upper-middle-class neighborhood into a chaotic scene: rubble, broken glass, bewildered people, bleeding victims and ambulances wailing through the streets.
Cries of people trapped under rubble could still be heard three hours after the missile struck, and army rescue teams were conducting "intensive operations" to pull them out, Israel Radio said.
In addition to the casualties, there were several narrow escapes.
The Ichilov Hospital reported that a 90-year-old woman whose heart had stopped beating was revived in the emergency room. "She came as a dead person, and she is alive now," a hospital spokesman said.
Search dogs spotted three people trapped in rubble. They were hauled out.
A four-floor apartment house took a direct hit, yet some residents escaped with minor injuries - such as the 10 members of Avshalom Halachmi's family who were assembled for a reunion. "It's a miracle - a big miracle," he said.
Menache Shemesh, his head bandaged to cover a gash, said he was in his apartment a block or two away. "We were watching TV; we heard the siren; we
went to put on our masks; the house was destroyed, and our television exploded," he said.
Minister of Police Ronni Milo said: "We shall try to stop this as soon as we can. The civilian population cannot go on longer under this kind of attack."
And Israeli Ambassador Zalman Shoval said in Washington that the Israeli cabinet would meet this morning to decide what to do.
Hours before the Scud struck, Defense Minister Moshe Arens warned: "If attacked, we will respond." The United States has feared - and Hussein is hoping - that Arab allies will desert the anti-Iraq coalition if Israel enters the war.
In an obvious reference to the United States, which has urged continued Israeli neutrality, Arens added: "Our actions that would be taken in the defense of Israel are really not contingent upon receiving permission from anyone."
And after yesterday's attack, Brig. Gen. Nachman Shai vowed that "we are at war here. . . . I can assure you we are not going to tolerate such things."
But the Israeli military spokesman added: "We have a lot of patience. We'll figure out the time and place what to do. . . .
"To the best of our knowledge, two Patriot missiles missed the Scud missile. . . . It was not intercepted."
"They were fired, they did not hit. They will hit the next time I hope, if there is" a next time, Shai said.
Late last week, two Patriot batteries staffed by about 150 U.S. military personnel were rushed to Israel after two Scud attacks on Friday and Saturday nights left 30 people with minor injuries. Four people suffocated because they failed to properly adjust their gas masks.
Each Patriot system has 32 missiles, but each can cover only a small area of the sky, Pentagon spokesman Pete Williams said yesterday.
U.S. technicians operate the computers and fire the missiles, according to Williams, but Israeli officers decide where the systems are located. Thus both nations share responsibility for the success - or failure - of each shot.
Israel also has Patriot batteries, acquired from the United States in September. But the Israeli soldiers who will operate them just returned after taking part in a U.S. Army training program at a base in the United States.
In addition, several members of the U.S. Congress said yesterday that Israel would shortly have five to six U.S. Patriot systems in place and that, in the near future, 12 systems would be operational. The legislators spoke after attending a closed-door briefing by Pentagon officials.
Until the gulf crisis began in August with the Iraqi invasion of Kuwait, the Israelis had shown little interest in buying the Patriot system from the United States because they were trying to develop their own antimissile system, the Arrow.
But after the invasion of Kuwait, the Israelis realized their Arrow system would not be ready for the impending gulf crisis and they turned to the United States for the Patriot.
Yesterday's successful Scud attack is likely to temper the euphoria that the Patriot was a perfect shield.
Prophetically, Arens warned several months ago that "no one has an answer today to the threat of ballistic missiles."