CAIRO, Nov 19 (Reuters) - Egypt's prime minister said on Monday that an agreement brokered by Cairo to stop the fighting between Israel and the Palestinians in Gaza could be close.

"Negotiations are going on as we speak and I hope we will reach something soon that will stop this violence and counter violence," Prime Minister Hisham Kandil said in an interview in Cairo for the Reuters Middle East Investment Summit.

Israel launched an air campaign on Wednesday with the declared goal of deterring Hamas, the Palestinian Islamist group that runs the Gaza Strip, from launching rockets at its southern communities.

Egypt is seeking to reinstate a ceasefire after an informal one it brokered in October collapsed.

"I think we are close, but the nature of this kind of negotiation (means) it is very difficult to predict," he said.

Egyptian President Mohamed Mursi had said on Saturday that there were "some indications" a ceasefire could be reached soon but said there were no firm guarantees.

"President Mursi is determined to play his role as a key player in the region and help mediate this," said Kandil, who visited Gaza on Friday to show Egypt's solidarity with the Palestinians.

Israel bombed dozens of suspected guerrilla sites in Gaza, ruled by the Islamist Hamas movement, on Monday and Palestinian rocket fire from the enclave eased off.

The prime minister said Egypt was in contact with both Israeli and Palestinian officials, and with other regional and international players, including Turkey and Qatar, as well as the United States, Britain and Germany.

"There are exchanges of visits and talks with both sides and there is also communications with various leaders from the region," he said.

Separately on Monday, another Egyptian official, who declined to be identified, said that Egypt was receiving "encouraging signals" about a ceasefire and said both Israel and Hamas were seeking guarantees.

"What we are trying to agree on is to achieve a ceasefire and achieve some possible guarantees, and then later discuss more guarantees," the official told Reuters.

Izzat Risheq, aide to Hamas politburo chief Khaled Meshaal, wrote on Facebook that Hamas would enter a truce only after Israel "stops its aggression, ends its policy of targeted assassinations and lifts the blockade of Gaza".

Listing Israel's terms, Vice Prime Minister Moshe Yaalon wrote on Twitter: "If there is quiet in the south and no rockets and missiles are fired at Israel's citizens, nor terrorist attacks engineered from the Gaza Strip, we will not attack."