"I would like to say that we are working to secure Shalit's release and that these efforts will soon bear fruit. We are optimistic. He will be released soon," Abbas told the France 24 news channel.
Shalit was abducted in a cross-border raid near the Gaza Strip on June 25 by gunmen from three Palestinian groups, including the armed wing of Hamas, and there has been no sign of life from him since.
Gilad Shalit and his father Noam (Reproduction)
"I am convinced we must free the soldier Shalit. He cannot remain imprisoned all this time," he said in the interview to be broadcast later Friday.
"At the same time, we say to the Israelis that they must free the Palestinian prisoners. But one thing does not depend on the other. Shalit must be released."
Abbas also said he was "certain" that abducted British BBC correspondent Alan Johnston was alive and would be "released shortly".
Step-by-step progress"We are in permanent contact with the British government, with the foreign ministry. We have discussed with them the conditions of his (Johnston's) kidnapping and his release," Abbas said.
"We are progressing step by step and I am absolutely certain that he will be released shortly, and of course, that he will go home," the Palestinian leader said.
Johnston, 44, is now in his fourth week of captivity after he was abducted at gunpoint in Gaza City on March 12 -- the longest a kidnapped westerner has been kept in the increasingly lawless territory.
Pressure on Palestinian leaders to secure Johnston's release has mounted in recent days as local journalists staged rallies in the West Bank and Gaza and declared a three-day reporting boycott on all government activities.
Johnston was the British broadcaster's main correspondent in Gaza for the past three years. His posting in Gaza is due to end this month.