Restrictions have been imposed on traffic in the area around his Ramallah office and snipers have been placed in buildings near his West Bank residence, officials said.
"We have information there are plans to kill President Abbas," a senior Palestinian source said on Monday, declining to give any details.
Some officials said assassinating Abbas would help Hamas, since the speaker of the Hamas-led parliament would automatically become president, in line with the Palestinian basic law or constitution.
Meanwhile, Israel's Haaretz newspaper reported that another militant group, Islamic Jihad, was plotting to kill Abbas with a car bomb.
"Sources close to Abbas reported the matter in talks with Israeli security officials," the Haaretz Website reported on Monday.
Islamic Jihad described the report as Israeli lies and Palestinian political analysts questioned whether the group would want to kill Abbas.
"We have information there are plans to kill President Abbas"
Palestinian security official
Unlike Hamas, Islamic Jihad has continued suicide bombings in Israel despite the truce.
"There is no difference between us and President Mahmoud Abbas that would make anybody even think of throwing a stone on him," said Khaled al-Batsh, an Islamic Jihad leader in Gaza.
Palestinian officials said that last month security forces discovered a 20-metre tunnel dug beneath Abbas house in Gaza and they suspected it was linked to an assassination plot by Hamas members.
Hamas, which won control of the Palestinian government earlier this year, denied any involvement.
Earlier this month a report in Britain's Sunday Times newspaper said a cell from Hamas' Izzedin al-Qassam armed wing planned to kill Abbas during a visit to the Gaza Strip.
Abbas' loyalists and Hamas gunmen
have clashed in recent weeks
The newspaper said Israeli intelligence got wind of the plot and warned the Palestinian leader that his life was in danger.
Abbas cancelled his planned visit, it said.
A senior Israeli security source confirmed that Israel suspected a plot to kill Abbas, who wants statehood talks with Israel.
Tension has been growing between Hamas and Abbas's Fatah faction over control of Palestinian security forces and the near bankrupt Palestinian Authority's finances.
Several Palestinians have been killed in clashes between Abbas loyalists and Hamas gunmen.