The Israeli prime minister has indicated he is ready to release large numbers of Palestinian prisoners if militants hold their fire during Israel's withdrawal from the Gaza Strip this summer.
Mr Sharon said Palestinian leader Mahmoud Abbas stressed during their meeting earlier this week that the release of long-serving prisoners is a top priority.
A newspaper report today quoted Mr Sharon as saying he told Mr Abbas that if the Gaza withdrawal proceeds smoothly, he would release larger numbers of Palestinians involved in attacks.
Israel is concerned that militants will fire on Israeli troops and Jewish settlers during the withdrawal to portray it as a retreat under fire.
Mr Abbas has secured promises from the armed groups that they will observe a truce, and the Israeli and Palestinian leaders declared an end to hostilities at their summit.
Mr Abbas is due to visit Gaza today to try to cement the ceasefire in talks with militant leaders.
The leaders of Hamas and Islamic Jihad have privately given their word to Egyptian mediators that a truce would be observed, although in public representatives of the militant groups have distanced themselves from Mr Abbas's truce declaration.
Local gunmen have said they would respond to any perceived Israeli violations.