In a condom-related spat that is seen by some as a proxy war between liberals and conservatives in the Catholic church, Francis last month appointed a five-strong team to examine recent turmoil at the Order, a Church-linked charity body descended from the crusading knights of the Middle Ages.
The Knights' hierarchy is currently refusing to cooperate with the probe. They say the dismissal last month of the Order's number three, Grand Chancellor Albrecht von Boeselager, is an internal affair of a sovereign entity which the Church has no reason to interfere with.
And the increasingly public row took a new twist with the leaking of a letter written by the Order's Grand Master, Matthew Festing.
In the letter, Festing claims three of the Vatican's appointees have “personal and financial” links to a Geneva-based fund in which the Order also has a stake.
As the sacked Grand Chancellor previously oversaw the Order's interest in the fund, this creates a potential conflict of interest, Festing writes in the letter without elaborating.
The letter appears to have triggered a statement from the Vatican on Tuesday in which Francis reiterated his confidence in the investigative team and rejected “all attempts to discredit the members of this group and their work.”
Von Boeselager's dismissal has been widely interpreted as being the result of him being too liberal for the tastes of Raymond Burke, the American cardinal who has acted as the Vatican's liaison with the Holy See since being sidelined from more important roles by Francis.
Burke is a prominent conservative figure who has been outspoken in his criticism of Francis's efforts to reform Church teaching on questions related to the family, marriage and divorce.
Reports in the specialist Catholic press have suggested Boeselager was targeted because of a row over the use of condoms in Africa to prevent the spread of AIDS – something conservatives say violates Church teaching but has been deemed acceptable by Francis and his predecessor Benedict XVI.
The Order of Malta was founded in Jerusalem in 1048 as a community of hospitals caring for the sick.
It was recognized by the pope in 1113, and now operates in 120 countries, managing hospitals and clinics, with 13,500 members and 100,000 employees and volunteers.