Israel Radio and Channel 2 TV reported Sunday that Zinni made his comments during a joint security meeting between Israeli, Palestinian and American officials in Jerusalem.
When Zinni arrived in Israel, he said he would stay as long as it took to broker a stable cease-fire.
A senior Israeli security source who spoke on condition of anonymity said Zinni's remarks were "not an ultimatum but something similar."
A U.S. official, who spoke to United Press International on condition of anonymity said: "The General has no plans to leave. He has no departure date." However he, too, confirmed Zinni was frustrated at the lack of progress in reaching a peace agreement.
Chief Palestinian negotiator Saeb Erakat said a Zinni departure would be "a catastrophy. We need the help of the Americans."
Erakat said the Palestinians were fulfilling all their obligations, but senior Israeli defense officials maintained Arafat has not changed his strategy.
"It is necessary that Zinni continues his mission because the alternative for this mission is more bloodshed between the two sides," said Tayeb Abdel Rahim, Yasser Arafat's chief of staff.
He added that if Zinni ended his mission to the region it "would help the extremists and the enemies of peace achieving their goals."
Prime Minister Ariel Sharon Sunday told his cabinet Israel "may have to increase its activities" in the wake of Palestinian attacks.
Sharon spent part of Sunday at Israeli military headquarters of the so-called Judea and Samaria Division at the Israeli settlement of Beit El, north of Ramallah in the Palestinian West Bank.
Military Chief of General Staff Lt. Gen. Shaul Mofaz told the ministers that the Palestinians were trying to create an impression there has been a change but he said that change was tactical.
A defense official, who briefed reporters in Jerusalem, pointed to his forehead and said he wanted to see "whether the diskette was changed (with Arafat). Has the intention changed?"
He hinted a shift in Israeli policy about pre-conditions for negotiating with the Palestinians, saying, "I am not going to run after every bullet."
In the past, Sharon has always insisted on a week long period of "absolute quiet" before any talks can begin.
Last week Foreign Minister Shimon Peres spoke to Arafat on the phone and Defense Minister Binyamin Ben-Eliezer received Arafat's economic advisor Mohammad Rashid.
"On course he came on Arafat's behalf," the defense source said. Ben-Eliezer told Rashid he wanted peace, a ceasefire, and to find a way to get both sides back to the negotiating table.
Meanwhile, however, a suicide bomber blew himself up in Haifa Sunday and the source noted that other attacks continue.
The source said the Israelis had given Zinni a list of 33 people whom he described as "ticking bombs."
The list does not include the names of Tourism Minister Rehavaam Zeevi's assassins. It does include the names of people Arafat has to arrest "if the man wants to stop (future) terror."
"He should detain them and hold them not under conditions of a five star hotel," the source continued.
Arafat should do what the Israelis do when they catch suspected terrorists: interrogate them, find out their missions and their contacts.
So far only 10 people of that list were detained, he said.
The source said he did not believe Arafat's regime would be in jeopardy if he cracks down on the Hamas and Islamic Jihad militants.
"Arafat is strong and the Tanzim is strong," he said, referring to the militia associated with Arafat's Fatah party. "The Tanzim is the biggest and most organized force."
Asked why the Israelis were striking at Palestinian Authority security targets and not at Hamas and Islamic Jihad, the source said: "Hamas has no bases. The Islamic Jihad has no bases. Their headquarters (comprise) cellular phones and meetings in (private) homes. I am not ready to hit civilian homes."
(Saud Abu Ramadan in Gaza contributed to this report)