John Kerry, the US secretary of state, is engaged in intense efforts to coax reluctant Israeli and Palestinian leaders towards an agreement to end their decades-old conflict, against the unhelpful backdrop of mounting political pressure on both sides to reject concessions.

Kerry is shuttling between Jerusalem and the West Bank city of Ramallah this weekend for a series of separate meetings with the Israeli prime minister, Binyamin Netanyahu, and the Palestinian president, Mahmoud Abbas.

His tenth trip to the region since March last year has coincided with an anxious expectation in Israel of the imminent death of former prime minister Ariel Sharon, who is suffering multiple organ failure after being in a coma for eight years.

Kerry is discussing a US-authored "framework agreement" with the two leaders, which is intended to set parameters for further negotiations in the hope of reaching a final deal. It covers the issues of a border on the basis of the 1967 line, refugees, security, Jerusalem as a capital for both states, and recognition of Israel as a Jewish state.

"We know what the issues are and the parameters," Kerry said when he arrived in Jerusalem on Thursday. "The time is soon arriving when leaders will have to take tough decisions. In the weeks ahead both sides will have to make tough choices." The current series of meetings was intended to "narrow differences on a framework that will set guidelines for negotiations", he added.

Neither leader will be asked to formally sign the framework agreement. US officials are reportedly undecided on whether to make its contents public, wary of creating a political backlash among critics of the negotiations process.

The framework agreement may lead to an extension to the negotiations timeframe. The current deadline for reaching a final deal is April, but almost no one expects that to be met. Netanyahu is reported to be pressing for an additional 12 months of talks; the Palestinians are opposed to any extension. An extra six months is a likely compromise.

But rightwing MPs from Likud – the party led by Netanyahu – and Jewish Home, a key coalition partner, have called for the framework agreement to be rejected by the Israeli leader. Naftali Bennett, the leader of Jewish Home, told Netanyahu in the past week that his party would not stay in the coalition if red lines were crossed.

Eight Israeli ministers backed a parliamentary bill calling for the de facto annexation of the Jordan Valley, a swath of land in the West Bank which has become a key factor in Israel's demands relating to security. Although it is unlikely to be passed, the support of key ministers is indicative of the hostility at the heart of the Israeli government towards Kerry's initiative.

On the Palestinian side, Abbas faced demands this week from the Palestine Liberation Organisation executive committee to walk out of negotiations and resume the strategy of signing Palestine up to global bodies such as the International Criminal Court.

On Friday, the secretary of state was greeted in Ramallah by demonstrators chanting "Kerry go home". In a statement, senior official Yasser Abed Rabbo described the framework agreement as a "worthless piece of paper". The Palestinian chief negotiator Saeb Erekat has said Israel is not interested in reaching a final deal.

Many analysts have pointed out that resisting pressure in their respective political backyards and settling the conflict will require enormous strength and courage from both leaders, qualities which each has to this point conspicuously lacked.

The attention focused on former Israeli premier Ariel Sharon in the past few days, as doctors warned of his impending death, has inevitably revived comparisons between the "warrior" leader and his old adversary Netanyahu.

Sharon, an uncompromising rightwinger, confounded the world by dismantling the Israeli settlements he had established in Gaza, and effecting a military withdrawal in the face of stiff opposition.

"When Sharon reached a dead end, he could find a way out by taking bold steps. But for Netanyahu, instead of doing the bold or unexpected thing, everything is about his political survival," said Uri Dromi, a political analyst and former government official.

"Israelis are now feeling emotional about the imminent loss of a hero, a giant, the last of the generation that fought to create our state. And they are lamenting the poverty of the current leadership."