The 83-year-old Abbas has endured a series of recent health scares which have revived anxiety over who will succeed him.
A senior Abbas aide, speaking on condition of anonymity in line with protocol, said the Palestinian leader was diagnosed with a fever on Sunday.
Abbas had an ear operation last week, and returned to the hospital late Saturday for a follow-up.
Saed Sarahneh, of Istishari Arab hospital, said late Sunday that "all tests are normal and his condition is reassuring." He did not elaborate.
Another Palestinian official, speaking anonymously because he was discussing the president's health, said Abbas has pneumonia and is on a respirator and is receiving antibiotics intravenously. He said he is conscious and lucid.
Abbas, who is a heavy smoker and overweight, has a long history of health issues, ranging from heart trouble to a bout with prostate cancer a decade ago. Two years ago, he underwent an emergency heart procedure after suffering exhaustion and chest pains. He suffers from arterial plaque and has had stents implanted.
Abbas took over as a caretaker leader following the death of Palestinian leader Yasser Arafat in 2004, and was elected for what was supposed to be a five-year term the following year. He has remained in firm control since then, refusing to designate a successor while a political split with rival Hamas prevented new elections.
Palestinians have been split since the Islamic militant group seized Gaza in 2007 after winning legislative elections a year earlier, ousting forces of Palestinian President Mahmoud Abbas who now governs just parts of the West Bank.
Repeated attempts at reconciliation have failed.
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