In 2009, the government said existing legislation would be amended so that children's conversion required the consent of both parents.
But amendments put forward in parliament this week retain a provision that a minor below 18 can convert to Islam if "his parent or guardian" consents.
The Malay-language text of the new law says the consent of "mother or father or guardian" is required.
Interfaith group Malaysian Consultative Council Of Buddhism, Christianity, Hinduism, Sikhism and Taoism said in a statement that the Federal Territories Bill -- effective for the capital Kuala Lumpur -- was unconstitutional and should be withdrawn.
The Malaysian Bar Council also said that "unilateral conversion of minor children to any religion by a parent, without the consent of the non-converting parent, is contrary to our constitutional scheme".
Government officials could not immediately be reached for comment.
It was not clear why the government has proposed the amended bill now, but lawyers said it could be part of a general overhaul of the decades-old law.
Conversion is a sensitive issue in Malaysia, where around 60 percent of 28 million people are Muslim Malays, with sizeable non-Muslim ethnic Chinese and Indian minorities.
Conversions of children and "body-snatching" cases -- where Islamic authorities tussle with families over the remains of people whose religion is disputed -- have raised tensions in past years.
Under Sharia law, a non-Muslim parent cannot share custody of converted children.
Non-Muslims also complain that they do not get a fair hearing when such cases end up in the religious courts set up to administer civil matters for Muslims.
