Cardinal Tarcisio Bertone, the Vatican's Secretariat of State, made the request for the formal dress in a letter released during last month's Synod of Bishops.
It came at the bequest of Pope Benedict XVI, reports a posting at veteran Italian journalist Sandro Magister's site at the Italian newsmagazine l'Espresso.
Bertone's letter, first made public Monday but dated Oct. 15, asks bishops and cardinals "kindly to guarantee" the observance of a 1982 letter by Pope John Paul II on the matter.
That letter, written by the deceased pontiff to the then-vicar general for the diocese of Rome, asked that priests wear the more formal dress as a "distinguishing mark" which contributes to "the beauty of the priest in his external behavior."
Bertone, according to a translation at Magister's site, asks the bishops and cardinals to recall "the duty of wearing regularly and with dignity the proper habit, in every season, partly in obedience to the duty of exemplarity that is incumbent above all upon those who render service to the successor of Peter."
"The very example of those who, sealed with the episcopal dignity, are faithful to the daily use of the cassock proper to them, during office hours, becomes an explicit encouragement for all, including for the Episcopates and for those who visit the Roman Curia and Vatican City," Bertone writes.
While typically seen worn by bishops and cardinals, priests in many parts of the world are more often seen instead wearing button down shirts with clerical collars.
When worn by bishops and cardinals, the cassock traditionally has a colored trim, with purple for bishops and red for cardinals.
October's synod of bishops, which saw prelates from across the world gather in Rome, was focused on what Pope Benedict has called the "new evangelization."
Bertone's letter does not explicitly mention women religious who visit or serve in Rome, but it does mention "religious" in a broad sense, asking for observance "of all ecclesiastics and religious."