Vatican Radio reiterated the stance, saying that "the question of the veil for Islamic women" should be "considered in the context of respect for the laws of the countries which welcome them".
Martino's comments come two weeks before the pope begins a visit to Turkey.
Although a secular state, Turkey has long wrestled over whether Muslim women should wear Islamic headscarves in such places as universities and public offices, where the article of clothing has been banned for many years.
"Dialogue is needed with our brothers"
Cardinal Renato Martino, former Vatican envoy to the UN
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Flanking the cardinal, Agostino Marchetto, another Vatican official who deals with immigration issues, referred to Italy's law requiring people to keep their faces visible in public.
The law dates to Italy's crackdown on domestic terrorism several decades ago.
Marchetto said Italy "rightly" has such a law and that obeying it is "part of accepting the law of this country".
Marchetto said: "Dialogue is needed with our brothers to make them understand the consequences of some of their desires, such as their own cultural and religious traditions, would not be positive in the society they are now in."
Martino also pushed the Vatican's campaign for Christians' right to worship around the world.
He lamented that some countries do not allow immigrants from Christian countries to profess their faith easily.