Over the weekend he received blood transfusions to increase his platelet count, but tests show he is suffering from mild kidney failure, which is said to be under control.
The Pontiff is said to have had a peaceful tenth night in hospital but is suffering from mild kidney failure after being admitted earlier this month with breathing difficulties.
On Sunday, the Holy See Press Office said: "The thrombocytopenia remains stable; however, some blood tests show early, mild renal insufficiency, which is currently under control.".
With both the Pope's decreased platelet count and mild kidney failure under control, the prognosis remains reserved, doctors have said.
The Pontiff was well enough to attend Mass in his hospital apartment on Sunday alongside his doctors and nurses, the press office added.