Al Qaeda operations in the Palestinian areas could have dire consequences for the entire region, Abbas told the Arabic language Al Hayat newspaper, published in London.
"We have signs of an Al Qaeda presence in the West Bank and Gaza," Abbas said, without elaborating. "We haven't yet reached the stage of capturing them."
Abbas said he had not expected the group would succeed in setting up operations in the Palestinian areas.
"The infiltration of Al Qaeda can ruin the whole region," he said.
Israel has warned that Al Qaeda was operating in the Gaza Strip, and arrested a Palestinian allegedly working with the group.
Israel withdrew from Gaza in September, relinquishing control of the border crossing with Egypt through which many Palestinians enter Gaza.
Al Qaeda leader Usama bin Laden has repeatedly cited Israel as a target, and the Palestinian cause as one of the reasons for the network's attacks.
Last year, Jordan's King Abdullah said he was convinced Al Qaeda had set up terror cells in Israel.