Prime Minister Ehud Olmert on Sunday rejected Hamas' offer of a cease-fire in the Gaza Strip, saying the government would not hold talks with the Islamist group until it recognizes Israel.

Olmert's comments came as three Qassam rockets fired by Palestinian militants struck the western Negev, causing no damage or injuries.

"The State of Israel has no interest in negotiating with entities that do not recognize the Quartet demands," said Olmert during the weekly cabinet meeting.

The Quartet of Middle East negotiators - the United States, European Union, United Nations and Russia - have demanded that Hamas recognize Israel, renounce violence, and accept previously signed agreements between Israel and the Palestinian Authority.

"Whoever accepts the Quartet principles will, in principle, be a partner for negotiations," Olmert said. "Whoever isn't willing to do so, to our regret, cannot be a partner for dialogue with us. This policy will not change."

"Our security forces have for months conducted numerous operations in the Gaza Strip, in order to reduce to a minimum the Qassam rocket fire, which has plagued the residents of the South, and in order to target those responsible for the Qassam fire," the prime minister added.

"The operations against terrorist groups will continue as it has been for months," he continued. "There is no way to describe what is taking place there other than as a real war between the IDF and terrorist groups."

"This war will continue, while making sure to avoid a humanitarian crisis that could harm civilians who are not at all involved in terrorism," said Olmert. "This policy requires patience and resiliency."

Defense Minister Ehud Barak briefed the cabinet ministers on security developements in Gaza and, contrary to Olmert, hinted at the possibility of a cease-fire with Hamas.

"If they stop firing, we won't be opposed to quiet," the defense minister said. "Hamas' consideration of a hudna [truce] stems from our effective operations and targeted killings."

Barak added that "there is no basis for political negotiations with Hamas if we want a continuation of Annapolis and a state in the foreseeable future. Hamas needs to be brought down, not saved."

Barak also said that, "In Israel's eyes, the Quartet's conditions- recognition of Israel and an end to terror and recognizing previous agreements- are all valid."

Hamas spokesmen and officials have made conflicted statements in recent days on the group's willingess to accept a cease fire. On Sunday, the organization did not rule out a future cease-fire if Israel first stops "all forms of aggression" against the Gaza Strip.

"If the occupation commits itself to stopping all forms of aggression against our people, only then the factions may discuss this issue," Hamas official Sami Abu Zuhri said. "But until then, there is no discussion among the factions over a calm."

Barak, Mubarak to discuss truce, Shalit in Egypt Wednesday

Defense Minister Ehud Barak is scheduled to meet Egyptian President Hosni Mubarak in Sharm el-Sheikh on Wednesday to discuss efforts to reach a temporary truce between Israel and Hamas.

On his one-day visit, Barak will also meet with intelligence chief Omar Suleiman and Defense Minister Mohammed Tantawi.

The two sides will also discuss the problem of arms smuggling from Egypt into the Gaza Strip and the negotiations to secure the release of kidnapped Israeli soldier Gilad Shalit, who is being held in Gaza.

This will be Barak's first visit to Egypt since taking office last June. Several attempts were made over the past few months to arrange such a visit, which was repeatedly delayed. Israeli defense officials said that a time has not been confirmed for the meeting at Sharm el-Sheikh.