Gilad Shalit was the gunner on a tank when it was attacked
Cpl Gilad Shalit, 19, was seized in an attack on an Israeli military post near Gaza on 25 June.
The armed wing of militant group Hamas swiftly rebutted Mr Abbas' comments.
Israel has launched regular air strikes and military incursions into the Gaza Strip to try to force the soldier's release, killing 140 Palestinians.
One Israeli soldier has also been killed in action.
Denial
Mr Abbas spoke in Rome at a news conference with the Italian Prime Minister Romano Prodi.
"I told the prime minister that as far as the question of the abducted Israeli soldier is concerned efforts are undergoing continuously that lead us to believe that the solution will be imminent," he said.
Efforts are being exerted but I wouldn't jump to any premature conclusions at this stage
Saeb Erekat
Palestinian negotiator
Palestinian negotiator Saeb Erekat also played down Mr Abbas' comments, suggesting that they had been taken out of context.
"I do not think that the president meant to say that the release was imminent. Efforts are being exerted but I wouldn't jump to any premature conclusions at this stage," he told CNN.
Cpl Shalit was abducted when Palestinian militant groups launched a surprise joint assault on an Israeli army position at Kerem Shalom, just outside the Gaza Strip.
Two soldiers were killed in the attack, and Cpl Shalit was seized and taken back into Gaza.
Hamas has denied claims made by Palestinian President Mahmoud Abbas that Israeli soldier, Gilad Shalit, 19, captured on June 25, will be released.

"Nothing has changed in the case of the Israeli soldier. The file remains in the hands of the resistance factions and not in the hands of any politician even if that politician is Abu Mazen Mahmoud Abbas. We heard this news from the press and our stance remains as it was: The case is in the hands of resistance fighters," said spokesman for the Izz el-Deen al-Qassam Brigades, Abu Ubaida.

Ubaida also said that handing over the soldier doesn't come "free. No politician dares to demand handing the soldier over without a return."

Abbas was quoted as saying earlier in a press conference, held in Rome, by an Italian translator that talks were leading to an "imminent solution" that would allow for the release of the soldier. "With regards to the issue of the abducted Israeli soldier, I have reiterated that there are ongoing efforts that lead us to believe in an imminent solution. I hope that the soldier is in good health and can soon return to his family," said Abbas, according to the official Italian translator.

However; the Associated press quoted Abbas as saying that "intense negotiations" were taking place.