"He is doing fine but still needs to take care," the spokeswoman for the Istishari Arab Hospital near Ramallah in the occupied West Bank told AFP.
"Until now there is no news about a timeframe for when he might leave."
Pictures and video of 83-year-old Abbas walking around the wards and reading a newspaper were published late Monday, in an apparent attempt to calm rumours that his condition was more serious than reported.
Ahmad Tibi, an Israeli Arab member of parliament, said on Twitter he had visited Abbas late Monday.
"He suffers from pneumonia and is treated with antibiotics," said Tibi, who is also a doctor, adding he was expected to spend "several more days" in hospital.
Abbas was admitted to hospital Sunday with a high fever. Last week, he underwent what was called minor ear surgery.
His health is the subject of regular speculation, with no clear successor identified.
In February, he underwent what was then described as routine medical tests in the United States.
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