Mr Abbas was speaking ahead of a ceremony where the Palestinian flag was raised at UN headquarters in New York for the first time.
The Palestinians have raised their flag at the United Nations for the first time, a symbolic gesture approved by a UN General Assembly vote last month.
The red, black, white and green Palestinian flag was raised early today in front of a packed crowd in the Rose Garden of UN headquarters in New York.
Palestinian president Mahmoud Abbas says the gesture is a call to Palestinians around the world.
"At this historic moment in the march of the struggle of the Palestinian people towards freedom and independence, I say to my people everywhere, if they are living, raise the flag of Palestine very high, because it is the symbol of our Palestinian identity."
Palestine is not a member of the United Nations, but the world body has permitted what it calls non-member observer states to fly their flags alongside those of full member states.
That came after the General Assembly adopted a Palestinian-drafted resolution.
The only non-member observer states are Palestine and the Vatican.
Last month, 119 countries voted in favour of the resolution, while eight, including Australia and Israel, voted against it.
UN Secretary-General Ban Ki-Moon attended the flag-raising ceremony.
He says the raising of the flag is a symbolic gesture.
"The symbolism of raising your flag at the United Nations reflects the commitment of the Palestinian Authority to pursue the long-held dream of the Palestinian people for their own state. It also symbolises the longstanding commitment of the United Nations to support Palestinian aspirations."
Mr Ban says, while the Palestinians still have a distance to go to achieve their dream, the moment should be seized.
"Achieving Palestinian statehood requires decisive action to advance national unity. The first step is ensuring that the West Bank and Gaza are integrated under a single authority. Now is the time to support initiatives which will preserve the two-state solution and create the conditions for a return to meaningful negotiations on the basis of an agreed framework."
Earlier, Mahmoud Abbas accused Israel of sabotaging United States efforts to broker peace.
In an address to the General Assembly, he warned Israeli security operations at Al-Aqsa mosque, one of Islam's holiest places in Jerusalem, could lead to a religious war.
"I call on the Israeli government, before it is too late, to cease its use of brutal force to impose its plans to undermine the Islamic and Christian sanctities in Jerusalem, particularly its actions at Al-Aqsa mosque, for such actions will convert the conflict from a political to a religious one, creating an explosive situation in Jerusalem and in the rest of the Occupied Palestinian Territory."
Mr Abbas says the Palestinian Authority no longer considers itself bound by the accords signed with Israel in the mid-1990s.
He repeated a long-held Palestinian Authority position that agreements do not apply as long as Israel supports West Bank settlements and will not release Palestinian prisoners.
The Palestinian president has called for a national unity government to unite the fractious Palestinian political scene.
"As for the internal Palestinian situation, we are determined to preserve the unity of our land and our people. We will not accept temporary solutions or a fragmented state. We will not allow this, and we will not allow those who are seeking to do this to do it. We, rather, will seek to form a national unity government that functions according to the program of the Palestine Liberation Organisation, and we seek to hold presidential and legislative elections."
Israeli-Palestinian strife has risen sharply in recent weeks as Arab states and Palestinians have accused Israeli forces of violations at Al-Aqsa mosque.
Mr Abbas's Fatah organisation controls the West Bank.
Hamas, which controls the Gaza Strip, is branded a terrorist organisation by Israel and the United States.
