Tzipi Livni went to Cairo at the invitation of Egypt's government
Israeli leaders have issued stern warnings to Palestinian militant group Hamas to stop rocket attacks on Israel.
Israeli Prime Minister Ehud Olmert said he would not hesitate to strike Hamas and another militant group, Islamic Jihad, in the Gaza Strip.
Foreign Minister Tzipi Livni warned Israel "cannot tolerate" Palestinian militants targeting Israeli citizens.
Some 50 rockets have been launched from Gaza in recent days, after the killing of three Hamas members by Israel.
A six-month ceasefire in Gaza between Israel and Hamas ended last week.
'Enough is enough'
Speaking after talks with the Egyptian leadership in Cairo on the failed ceasefire in Gaza, Ms Livni described the latest escalation as "unbearable".
Ehud Olmert appeals to the people of Gaza to turn against Hamas. Courtesy Al-Arabiya TV
"Hamas needs to understand that our aspiration to live in peace doesn't mean that Israel is going to take this kind of situation any longer. Enough is enough," she said.
The BBC's Christian Fraser says some will see the visit as the first of several diplomatic steps Israel must take before launching military action.
Mr Olmert called on residents of Gaza to stop militants "firing on innocent civilians", in an interview with the Arab television station Al-Arabiya.
"I say to you in a last-minute call, stop it," Mr Olmert said, Israeli media reported.
"Don't let Hamas, which is acting against the values of Islam, put you in danger. Stop them. Stop your enemies and ours."
Mr Olmert added: "I will not hesitate to use Israel's might to strike Hamas and [Islamic] Jihad. How? I will not go into details now."
Ms Livni had earlier been holding talks with Egypt's President Hosni Mubarak and Foreign Minister Ahmed Aboul Gheit, who brokered the ceasefire.
Mr Aboul Gheit urged restraint from both sides, and said Egypt would continue to act as a mediator but admitted that a new truce currently seemed unlikely.
Relations between Egypt and Gaza are strained, our correspondent says.
President Mubarak has told the militants he believes they are making a mistake in abandoning the ceasefire.
It is widely understood the Egyptians are furious with Hamas for boycotting peace talks with Fatah last month, which were due to be held in Cairo.
The question now, our correspondent says, is whether the Egyptians would back an Israeli military offensive against Hamas.
The London-based newspaper Al-Quds al-Arabi has reported that Egypt would not object to a limited Israeli operation in the Gaza Strip, aimed at toppling Hamas.
Ms Livni travelled to the Egyptian capital at the personal invitation of the government.
This is rare given that Mr Mubarak usually only meets Israeli officials in the Sinai resort of Sharm el-Sheikh.
It is being read as an Egyptian endorsement of Tzipi Livni, who is seeking to become prime minister in February's general election.
It has been noted that President Mubarak has not yet invited for talks the Defence Minister and Labour Chairman Ehud Barak, who is also a prime ministerial hopeful.