"Israel should refrain from unilateral acts including what Palestinians perceive as the provocative expansion of settlements, land confiscation, home demolitions, and confiscation of IDs," shetold Israeli high school students.
"We believe that a time-out from these kind of unilateral actions will create a climate in which an accelerated approach can succeed in achieving a final Israeli-Palestinian peace agreement," Mrs Albright said in comments certain to anger Israel's right-wing government.
Earlier, Palestinians listened with disappointment to the total priority given by Mrs Albright to Israeli security in her three-hour talks with Yasser Arafat, the Palestinian leader.
"We have got agreement that terrorists are terrible, but not yet on the best way to get the peace process back on track," Mrs Albright said at a joint press conference with Mr Arafat. Saeb Erekat, the chief Palestinian negotiator, said: "The gap between us and the Israeli government is as wide as ever."
The duet from Mrs Albright and Benjamin Netanyahu, the Israeli prime minister, about dealing with "terrorism" - and regarding the expansion of Israeli settlements and demolition of Palestinian houses on the West Bank as peripheral - was interrupted by Leah Rabin, the widow of Yitzhak Rabin, the Israeli prime minister assassinated in 1995.
"I have doubts about how much terrorism can be uprooted," she told Israeli radio before seeing Mrs Albright. "We were also terrorists once and they didn't uproot us and we went on dealing in terrorist activities. Despite all the efforts of the British army in the land we went on with terrorism."
Mrs Rabin was referring primarily to the campaign of the Irgun, led by Menachim Begin, which waged guerrilla war against British forces in Palestine in the 1940s. Mr Begin later became prime minister of Israel and leader of the Likud party which is now headed by Mr Netanyahu. Asked if the latter wanted peace Mrs Rabin said: "Allow me to express doubt. He does everything against it."
One concession to Palestinian grievances came over the issue of pounds 66 million tax revenues collected by Israel for the Palestinian Authority and withheld since the suicide bombing in Jerusalem on 30 July. Mrs Albright said it was "beyond her understanding how withholding money was a security issue". Mr Netanyahu said he was waiting to see action by Mr Arafat before handing over the money.
Most of the Palestinian demands concern Israel implementing the Interim Agreement signed in 1995 under which it pledged to end the occupation of most of the West Bank. They also want an end to the present closure of Palestinian towns and villages isolated by Israeli checkpoints. Israel wants a round-up of activists in Hamas, the Islamic militant organisation, by Mr Arafat.
The Likud party has reacted angrily to reports that President Ezer Weizman told Mrs Albright "to knock heads together" and to ask Mr Netanyahu to implement the Interim Agreement. Although officials say the president was quoted out of context, Likud is threatening to run a candidate against him in the next presidential election.
Just why the Palestinian leader would find it difficult to start mass arrests of Hamas was best explained by the presidential troops guarding the gate. "Albright only talks about Israeli security, but each one of us has a brother in an Israeli jail," said Imad, pointing to a scar on his head made by an M-16 round in the fighting in Ramallah last September.
Jamil, another member of the presidential guard, saidhe found Mrs Albright's visit humiliating and, in the long term, he expected more fighting.Reuse content