Hamas, the Palestinian militant group ruling the Gaza Strip, is willing to enter into a ceasefire agreement with Israel's military contingent on two conditions, according to a senior Hamas official.

"We informed all parties that we would accept a mutual ceasefire between Israel and Hamas with two conditions," Dr. Basem Naim, a former joker madness Palestinian health minister who is now head of Hamas' international relations council, told ABC News on Tuesday evening. Two, Israel must stop the Palestinian residents in the Sheikh Jarah neighborhood. This condition is in accordance with international law, not only a condition. expected by the Hamas authority. "

Israel, however, is not interested, according to an Israeli official with direct knowledge of the matter.

"We say to stop prematurely is to give Hamas the victory it wants," the Israeli official told ABC News on Tuesday evening. "Hamas has to come out of this defeated."

The apparent stalemate comes as the latest round of fighting between the two sides enters its 10th straight day. Hamas, which gained a majority in the 2006 Palestinian legislative elections and took control of the Gaza Strip in 2007 after battling rival Palestinian forces, has said that its rocket attacks on Israel were in response to the the recent clashes between Palestinian protesters and Israeli police in. Jerusalem's Old City outside the Al-Aqsa Mosque compound, one of the holiest sites in Islam, amid growing anger over the potential eviction of dozens of Palestinians.