International mediators are hoping to kickstart stalled cease-fire negotiations between Israel and Hamas with a new round of talks meant to finally clinch a deal between the sides. But the chances of a breakthrough appear slim.The new talks are set to begin Thursday, but Israel and Hamas have been mulling an internationally-backed proposal for more than two months that would wind down the 10-month-long war and free the roughly 110 hostages still held in Gaza.The indirect talks have not advanced substantively during that time and sticking points remain. New terms put forward have complicated progress. And Hamas has yet to say outright whether it will participate in the new round.Meanwhile, the fighting in Gaza rages on, the hostages continue to languish in captivity, and fears of an all-out regional war involving Iran and one of its regional proxies, Hezbollah, have surged. The killing of Hamas’ top leader in Tehran in an apparent Israeli attack further plunged the talks into uncertainty.Here is a look at the proposed cease-fire deal and why talks have stalled:What does the proposal look like?On May 31, President Joe Biden detailed what he said was an Israeli cease-fire proposal, calling it “a road map" to a lasting truce and freedom for the hostages. It set off the most concentrated U.S. push to bring about an end to the war, which was sparked by Hamas’ Oct. 7 attacks on southern Israel.The original proposal involved three phases. The first would last for six weeks and include a “full and complete cease-fire,” a withdrawal of Israeli forces from all densely populated areas of Gaza, and the release of a number of hostages, including women, the elderly and the wounded, in exchange for the release of hundreds of Palestinian prisoners. Palestinian civilians would be able to return to their homes and humanitarian aid would be increased.The two sides would use that six-week period to negotiate an agreement on the second phase, which Biden said would include the release of all remaining living hostages, including male soldiers, and Israel’s full withdrawal from Gaza. The temporary cease-fire would become permanent.The third phase would kick off a major reconstruction of Gaza, which faces decades of rebuilding from the devastation caused by the war.What are the sticking points?Even though Biden threw his weight behind the proposal, it has not led to a breakthrough and the sides appear to have grown further apart in the weeks since.Israel has been wary of the plan’s provision that the initial cease-fire would be extended as long as negotiations continued over the second phase. Israel seems concerned that Hamas would drag on endlessly with fruitless negotiations.Hamas has appeared concerned that Israel would resume the war once its most vulnerable hostages were returned, a scenario reflected in some of Prime Minister Benjamin Netanyahu's recent comments. Israel could also make demands during this stage of negotiations that were not part of the initial deal and would be unacceptable to Hamas — and then resume the war when Hamas refuses them.Israel has added additional demands to the initial proposal in recent weeks, according to two Egyptian officials with knowledge of the talks. In a statement Tuesday, Netanyahu's office denied this, calling the additional terms “essential clarifications.” It said Hamas has made 29 additions, without specifying which.The Egyptian officials said Israel seeks to maintain control of a strip of land along Gaza’s border with Egypt known as the Philadelphi corridor. Israel believes Hamas uses the area to smuggle in weapons through underground tunnels, which Egypt denies.Israel also wants to maintain forces along an east-west route that bisects Gaza so that they can weed out any militants crossing into the territory's north. Netanyahu's office has said Israel wants some way to ensure this, but it denied accusations that this was an additional condition. Hamas has rejected the idea, saying Israel would use it as a pretext to prevent Palestinians from returning to their homes.The Egyptian officials and Netanyahu's office said Israel also wants veto power over the Palestinian prisoners who would be freed. Hamas refuses to compromise on the issue, they said.Israel also wants a list of the hostages who are still alive — another condition rejected by Hamas, according to the officials, who spoke on the condition of anonymity because they weren’t authorized to discuss the sensitive talks with the media.What else is complicating progress?The talks were further thrown into disarray last month when a blast killed Hamas leader Ismail Haniyeh while he was in Tehran for the Iranian president’s inauguration. The attack was widely blamed on Israel, which has not confirmed or denied it. Biden said the apparent assassination had “not helped” cease-fire efforts, and the talks were driven into a deep freeze.That killing came just hours after Israel assassinated a top Hezbollah commander in a strike in Beirut. Both strikes drew threats of retaliation from Iran and Hezbollah, and the fear of an all-out regional war diverted international attention away from efforts to wind down the fighting in Gaza. The killings spurred a flurry of diplomatic activity and led the U.S. to direct military assets to the region.Both Netanyahu and Hamas' new top leader, Yahya Sinwar, have incentives to continue the war.Netanyahu's critics say he is dragging out the war for his own political survival. His far-right coalition partners have pledged to topple the government if he agrees to a cease-fire, what could trigger elections that might oust him from power. Netanyahu has said he has the country's best interests in mind.Hamas has gained from the international condemnation that Israel has faced because of the war. And on a personal level, Haniyeh's killing has shown that Sinwar's own life could be on the line if he surfaces once the war ends.___Magdy reported from Cairo.