Abbas arrived home in Ramallah from New York where he made a controversial request for Palestine to be recognized as an official state by the United Nations.
"Our international diplomatic resistance has begun and we have a long road ahead," Abbas said at his compound.
Abbas' request was opposed by the United States and Israel. Critics said changing Palestine's diplomatic status would derail the methodical four-nation negotiating process in the region and also add further credibility and clout to Hamas.
CNN said Abbas' supporters appeared to be solidly behind his move.
"We must know with certainty that there are those who will punish us," Abbas said. "There are those who will deny us justice and deny what is right but we will stand up to them."