Abbas said on Friday that he was convinced Sharon could bring peace to the Middle East if re-elected next March.
"There has been a radical change on the political map of Israel. We now have a really new situation," Abbas told a joint news conference after talks in Rome with Silvio Berlusconi, the Italian prime minister.
"I think that the Israeli people could opt for the choice of peace and when the will of the people is the same as the will of the elected leader, much can be achieved."
A man of conviction
Sharon quit the Likud party he founded to set up a centrist party which has spelled out its willingness to see the creation of a Palestinian state.
"Without doubt he is a man to realise his convictions," Abbas said.
However, he cautioned that the situation in Israel from the Palestinian point of view is still "very difficult to decipher" because of the changes within Likud, where there were many "new and unknown" faces.
Berlusconi reiterated an offer to host Israeli-Palestinian talks in the Sicilian town of Erice, and said Italy was ready to mediate if asked to by both sides.
Abbas, on a two-day visit to Rome, had talks earlier on Friday with Carlo Azeglio Ciampi, Italy's president, and has an audience with the Pope at the Vatican on Saturday.