Pope Francis, who is in critical condition in hospital battling double pneumonia, rested well throughout the night, the Vatican said on Tuesday.

The 88-year-old pope was admitted to Rome's Gemelli hospital on February 14.

"The pope rested well all night," the Vatican said in a one-sentence statement.

On Monday, the Vatican said the pontiff's condition remained critical but had shown a "slight improvement", adding that the "mild kidney insufficiency," first reported at the weekend, was not a cause for concern.

Double pneumonia is a serious infection that can inflame and scar both lungs, making it difficult to breathe. The Vatican has described the pope's infection as "complex," and said it was caused by two or more microorganisms.

Francis, who has been pope since 2013, has suffered bouts of ill health over the past two years. He is particularly prone to lung infections because he developed pleurisy as a young adult and had part of one lung removed.

Thousands of people gathered in St. Peter's Square on Monday evening to pray for the pope's recovery.

His friend, the Honduran cardinal Oscar Rodriguez Maradiaga, told La Repubblica newspaper: "I think...it's not time for him to go to heaven yet."

The pope signalled in early February that he had a bad cold, which meant he could not read out his speeches. Despite this, he continued to work, with multiple daily meetings and even taking part in open-air Masses, despite the chill.

Some well-wishers have said he should have taken better care of himself, but Maradiaga defended his work ethic.

"He is aware that he has a mission he must carry out, and nothing stops him. The pope explained that he did not accept his election (as pontiff) in order to rest," he said.

In Monday's statement, the Vatican said Francis had resumed working in his self-contained apartment within the Gemelli hospital, and had called the Catholic parish in Gaza, which the pope has done frequently during the Israel-Hamas war.