Sharon "told me he was ready to restart (the negotiations) but that the Palestinians were hesitant," Mubarak told national television on Saturday.
He was recounting the hardline Israeli leader's telephone call to him to congratulate him on the Muslim festival of Eid al-Adha, marking the end of the annual pilgrimage to Makka.
Mubarak has stepped up calls in recent days for renewed efforts to find a solution to the bloody and divisive 40-month-old conflict between Israel and the Palestinians through a floundering US-backed peace blueprint known as the "road map."
He said he had also contacted the Palestinian side to lobby them to open new talks.
"I spoke with the Palestinians yesterday (Friday) and told them they should establish contacts with the Israeli side to restart the negotiations," he said, adding that they had also assured him they would do so.
Palestinian and Egyptian sources said Mubarak had also spoken twice on Saturday with Palestinian leader Yasir Arafat, who told him he was taking steps to facilitate a first meeting between Sharon and Palestinian prime minister Ahmad Quraya.
"They discussed what to do in the next few days and weeks," Arafat aide Nabil Abu Rudaina said.
The Egyptian news agency MENA said Arafat, who is considered persona non grata by Israel, had pledged to establish contacts with the Israelis in order to agree on a date for a Sharon-Quraya meeting.
It added Arafat had called Mubarak back to inform him of the "steps he had taken in order to begin preparations for a meeting immediately after Mr Quraya's return" from a visit to Jordan.
Since he was named prime minister in September 2003, Quraya has not met Sharon despite a series of preliminary contacts between the two sides.