If I were the mediating countries, Egypt and Qatar, I would put an agreement on the table that takes into account some of Hamas's demands and some of Israel's demands, and I would say to Israel and to Hamas: TAKE IT OR LEAVE IT!
If Israel and Hamas decide to reject the proposed agreement, I would publish it publicly to show it to the world, and especially so that the Israeli people and the Palestinian people can see it. I would inform Israel and Hamas that we are done playing the game by their rules. The rules have changed - this is the agreement, the negotiations are over!
For more, an article by Gershon Baskin: