Marino, who arrived in Kuala Lumpur less than six months ago, had last Thursday waded into a religious row in Muslim-majority Malaysia over the use of the word "Allah".
He described arguments put forward by the Catholic Church in an ongoing court battle for the right to translate "God" as "Allah" in Malay-language Bibles and other literature as "logical and acceptable".
Soon after, hardline Muslim groups began calling for him to be sent home. Several cabinet ministers also accused him of "interference".
The statement from the archbishop's office said he had never intended to interfere.
"In that context, he asked him (Anifah) to convey apologies for any misunderstandings and inconveniences that it may have caused," the statement said.
Anifah also said in a statement that "Archbishop Marino was advised to be mindful of the religious sensitivities of the host country and that the issue he commented on is still under the Court of Appeal".
Controversy over the use of the word "Allah" came to a head three years ago, when the High Court ruled that non-Muslims are allowed to use the word to refer to God in their Malay-language literature.
The court case arose after Malaysia's Catholic Church sued the government for banning the use of the word in its weekly newspaper, The Herald.
Muslims had denounced the verdict, claiming "Allah" is exclusive to Islam. The government decided to appeal the ruling after several places of worship were fire-bombed.
Malaysia has more than 2.5 million Christians in a population of 28 million, of which about 60 percent are Muslim.
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