The two met on Monday to discuss forming a national unity government, but both leaders are expected to hold more meetings with their own supporters before negotiations start on forging a coalition.
A broad-based coalition government with Labour would give Sharon much-needed support as he pushes forward with his contentious plan to withdraw from the Gaza Strip.
But Sharon also risks alienating hardliners within his Likud party who oppose a union with the opposition.
The prime minister warned opposing members of his ruling coalition he could call early elections if they blocked his bid to widen his government to push ahead with the Gaza pullout plan.
West Bank control?
Masters of Survival
* The political roots of Peres and Sharon go back to the socialist Mapai party that was led by David Ben-Gurion, Israel's first prime minister.
* Sharon is an ex-army general who was dubbed "the Bulldozer" for his past role as cabinet minister in planting Jewish settlements on Palestinian land.
* Sharon, a founder of the Likud party in 1977, won elections to become prime minister twice - in 2001 and 2003. Born in 1928, he
followed a traditional route in Israel that took him from the
military into politics.
* Peres, as foreign minister under Labour Prime Minister Yitzhak Rabin, orchestrated interim peace deals with Palestinians in the early 1990s.
* Born in 1923, Peres was once described by Rabin as the
"indefatigable schemer" of the slain prime minister's political manoeuvrings.
Palestinians fear the planned Gaza pullout will consolidate Israel's occupation of the West Bank. Sharon's "disengagement plan" envisions dismantling all 21 Gaza Jewish settlements - illegal under international law - and four of 120 in the West Bank by 2005.
The two sides agreed on supporting the Gaza plan, said a senior political source.
"But it was still only the very beginning of negotiation and they did not discuss specific issues. Peres said he still has to get his party's mandate if Labour is to join a government," the source said.
Israel's cabinet approved the withdrawal project after Sharon fired two far-right ministers, but that cost the former general the majority in parliament he will need next year if he is to push through the phases of the plan.