Abbas, a favourite to win the contest, decided to go ahead with a campaign visit on Saturday to the southern Gaza Strip despite considerable uncertainty.
The PLO leader almost called off the trip because of Israeli military operations in the Khan Yunus refugee camp just north of Rafah, but went ahead apparently after receiving assurances from the Israeli occupation army that he could pass through Israeli roadblocks and checkpoints smoothly and safely.
His trip was delayed by two hours.
Abbas later dropped plans to visit Khan Yunus, the second biggest population centre after Gaza City, because of Israel's continuing military operations that have killed 12 Palestinians so far.
He was received by thousands in Gaza City, which has witnessed Israeli army incursions and the destruction of houses over the past four years of the second Palestinian intifada.
Abbas said: "Rafah continues to suffer oppression and the humiliation of occupation but it will not be defeated and not be humiliated."
"Rafah continues to suffer oppression and the humiliation of (Israeli) occupation but it will not be defeated and not be humiliated"
He told the cheering crowd: "We will not back down except after victory and the establishment of an independent Palestinian state, with Jerusalem as its capital."
UN refugee agency figures show at least 16,000 Palestinians have been made homeless by Israeli demolitions and military operations in the area.
Plea for unity
Abbas, also known as Abu Mazin, said: "We seek a good and safe life for our people. We want a state of law for the sake of every Palestinian."
Repeating campaign themes, he said he would work for the release of more than 7000 Palestinians languishing in Israeli prisons and the right of return for refugees forced to leave since the establishment of the Israeli state in 1948.
He also called for Palestinian unity.
Abbas was told he would not be
harassed at Israeli checkpoints
His aides have said he needs the support of the people in the street for a large margin of victory that would enable him to negotiate with Israel in the future.
However, Abbas is also signalling that he wants to co-opt other groups and movements, not confront them as Israel and the United States have demanded.
The campaigning has prompted questions and raised concerns among both Israelis and the Palestinians about whether Abbas is playing campaign politics or identifying with certain groups.