Addressing a special session of the Palestinian parliament in Gaza City on Tuesday, Abbas said Palestinians should conduct themselves during Israel's pullout in a way that showed the world they deserved a state.
He urged armed groups in the Gaza Strip to stop firing rockets on Israel in his keynote speech eight days before the evacuation.
"This must stop so that we can focus on security and economy," he said.
He also urged armed groups to honour a ceasefire with Israel, saying no one had the right to decide on his own to violate the understanding.
"If we feel this truce is no longer active ... we will agree on that and take a decision," Abbas told lawmakers.
"But no one can take this decision alone and say they are defending the Palestinian people," he added.
Abbas also warned against seizing property left by the Israelis and called on Palestinians to avoid excessive celebration.
The president also confirmed in his speech that the second Palestinian parliamentary elections would take place in January 2006, but did not give an exact date.
"This must stop so that we can focus on security and economy"
The elections were originally to take place in the middle of last month but were postponed due to wrangling over the rewriting of the electoral law.
Resistance group Hamas said it had reservations about the January date announced by Abbas.
"Those who feel committed to the Cairo agreement would have to be committed to holding the elections before the end of this year," said a Hamas leader, Mahmoud al-Zahar, referring to a deal reached by Palestinian factions late last year.
"We had agreed on the date of last January 17, and an official decree was issued to that effect. But regrettably, the decree has never been implemented," he said.
"Then at a meeting for the follow-up committee, less than a week ago, they introduced the dates of January 20, February 20 and March 20. Based on our sources, the elections would not be held in any of these dates. Trying to escape to unspecified dates in order to skip a period of time, is unacceptable to Hamas. This is why we had reservations on the January date," al-Zahar said.
But he affirmed the group would participate in the elections.
Israel is to uproot the 8000 settlers from Gaza and several hundred residents living in four northern West Bank colonies from 17 August.
It would be the first time that it has ever withdrawn from occupied Palestinian territory.
While Palestinians have welcomed Israeli withdrawal from any part of the occupied territories, they are also wary that Israeli Prime Minister Ariel Sharon will try to use the Gaza pullout to enable him to keep hold of large West Bank settlement blocs.
Abbas said he had raised these fears during a meeting with US President George Bush in May.
"We said we were concerned about [the Gaza pullout] compromising the final status solutions. Anything that deals with the final status should not be dealt with unilaterally," said Abbas.
"If we feel this truce is no longer active ... we will agree on that and take a decision. But no one can take this decision alone and say they are defending the Palestinian people"
"Our other concern was that Gaza would be the first and last and that there would be no linkage between Gaza and the West Bank," he added in reference to a Palestinian demand for safe passage between the two territories.
In his speech on Tuesday, Abbas also denied that asking other governments to give Palestinians living abroad citizenship was a capitulation on the right of return of Palestinian refugees - a key Palestinian demand in peace negotiations.
He said the call for citizenship was simply to facilitate ordinary living for Palestinians abroad.