Mr. Abbas defended the inclusion in the election of the militant Islamic faction Hamas, which refuses to give up its armed wing.
"We gave them a letter explaining our bad situation," he said, "and asking for aid to continue to the Palestinian Authority," now run by the militant faction Hamas.
Mr. Abbas's Fatah movement, which has dominated Palestinian politics for decades, is facing a strong challenge from the Islamic faction Hamas.
On Sunday, hundreds of Palestinians, including the prime minister from the militant faction Hamas, stayed around the house and on its balconies and roof throughout the day.
But the radical Islamist faction Hamas, which won the Palestinian parliamentary elections and is expected to assume power soon, has never accepted Israel's existence.
Fatah remains the favorite in the elections, but it is facing an increasingly strong challenge from the Islamic faction Hamas, which is competing for the first time.
Ismail Haniya, a senior leader in the Islamic faction Hamas, said the vote reflected Israel's desire to "continue the occupation of Palestinian land."
Meanwhile, the Islamic faction Hamas claimed responsibility for an attempted attack on a Jewish settlement in central Gaza late Tuesday night.
The Islamic faction Hamas claimed responsibility.
A powerful explosion at the house of a family linked to the Islamic faction Hamas killed four people when explosives detonated accidentally.