"They are freedom fighters and should live a dignified and safe life," said Abbas, whose call for a negotiated settlement has been rejected by some groups whose support he is courting in the 9 January elections for president of the Palestinian Authority.
Abbas said on Monday he was determined to ensure the rule of law prevailed in the Palestinian territories.
He said he would achieve that goal through dialogue and discussion as he pursued national unity.
"Palestinians taking up arms against each other will not happen," the leader of the Palestinian Liberation Organisation (PLO), also known as Abu Mazin, pledged.
Meanwhile, Israeli forces have killed a 22-year-old Palestinian who is said to have been a member of the Izz al-Din al-Qassam Brigades.
Aljazeera's correspondent in Palestine said: "Muhammad Yusuf Qandil, a member of the Izz al-Din al-Qassam Brigades, was killed when an Israeli tank shell hit his home in Jabalya refugee camp in Gaza Strip."
Izz al-Din al-Qassam Brigades had previously said it targeted a US-made Israeli tank with an explosive device in the town of Bait Hanun, in the Gaza Strip.
"This attack is said to have come as a response to the Israeli incursions into the area," said the correspondent.
"In another attack a Palestinian girl was seriously injured when Israeli forces fired randomly in al-Shabura refugee camp in Rafah."
Israeli forces in the meantime said they have partially withdrawn from the town of Bait Hanun, in the northern Gaza Strip, after an incursion with 50 tanks and military vehicles, backed by helicopter gunships.
At least 13 Palestinians have been killed since Israeli forces began the latest military operations in the area, withdrawing from Khan Yunus and starting with Bait Hanun on Sunday.
Israeli forces have left a trail of
destruction in Khan Yunus
The army said soldiers had redeployed or pulled out of the Bait Hanun area but took up positions "from which they can go back in if necessary".
Witnesses, however, said Israeli occupation forces that had invaded the area on Sunday and destroyed orchards and some homes had redeployed and did not withdraw completely, as earlier reports had indicated.
Abbas, in his campaign speech, said Palestinians were ready to make peace with Israel "built on justice and rights".
He repeated core demands, such as a right of return for refugees to homes now in the Jewish state, a demand long rejected by Israel.