(Releads with Israel saying offensive had damaged Hamas, previous JERUSALEM)

PARIS, Jan 1 (Reuters) - Israel's offensive in the Gaza Strip has damaged Hamas and will continue until the Jewish state no longer deems the Palestinian Islamist faction a threat, Israeli Foreign Minister Tzipi Livni said on Thursday.

"I think that even now, after a few days of operation we have achieved changes," she told reporters on a visit to Paris, referring to an air strike campaign launched on Saturday.

"We affected most of the infrastructure of terror within the Gaza Strip and the question whether it's enough will be according to an assessment on a daily basis."

Livni, who met French President Nicolas Sarkozy, said Israel intended to "change the reality" in and around Gaza. Israeli officials say this would entail ending Palestinian rocket salvoes that have sown panic in neighbouring southern Israel.

"We want to weaken Hamas in the Gaza Strip. At the end of the day, Hamas is a problem not only to Israel but to the entire Palestinian people," Livni said.

"They are a problem to all the Arab states who understand that they have their own radical elements back home, including Muslim brotherhoods in different places."

Hamas has remained defiant despite an Israeli barrage that has killed more than 400 Palestinians. Four Israelis have been killed by retaliatory rocket strikes.

Livni came to Paris to address a French proposal for a 48-hour truce to allow humanitarian aid into Gaza. Her office said she had reiterated her government's rejection of the idea.

"There is no humanitarian crisis in the Strip, and therefore there is no need for a humanitarian truce," the Foreign Ministry quoted Livni as saying in a statement.

In her remarks to reporters, Livni said Israel had been careful to protect the civilian population and had kept the humanitarian situation in Gaza "completely as it should be".

"The crossings are open, more than it used to be before the military operation," she said.

The European Union has called for an immediate ceasefire in the Gaza Strip, which Israel has been attacking for days in retaliation for rocket attacks on its territory from the Hamas-controlled area.

Sarkozy, whose country handed over the rotating EU presidency to the Czech Republic at midnight is due to visit Egypt, the Palestinian Territories, Israel, Syria and Lebanon on Monday and Tuesday, hoping to assist in ending hostilities.

Despite Israel's rejection of France's ceasefire proposal, Livni thanked Sarkozy for his engagement.

"President Sarkozy is well familiar with the situation and the complexity in our region. He understands the threat that Israel is facing," she said. (Reporting by James Mackenzie and Laure Bretton; Editing by Katie Nguyen)

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