The paper based the reports on sources who attended the four-way summit in Sharm el-Sheik Monday.
According to these sources, Abbas hoped that Barghouti's release would restore Fatah's popularity among the Palestinian public and give the movement a boost in the West Bank.
Abbas had other demands for Olmert at the summit. Sources said that he asked Olmert to drastically reduce IDF presence in West Bank cities, remove major roadblocks near cities and start lifting limitations on Palestinians' movement in the West Bank.
He also demanded that the Israeli government transfer the tax money it was holding, as agreed.
Mahmoud Abbas told al-Hayat reporters that he did not agree to the financial boycott on the Gaza Strip. This differs from the opinion, commonly held in Jerusalem, that Fatah wanted Israel to crack down even further on the Strip, thereby damaging Hamas.
Chief Palestinian negotiator Dr Saeb Erekat told the newspaper that out of concern for the wellbeing of the population in Gaza, he was working diligently with the Israeli teams to ensure all the necessary supplies were transferred into the Strip.
He added that he was trying to obtain guarantees from Israel that they would not stop the provisions from being delivered.