Negotiators have proposed a 40-day pause in the fighting and an exchange of hostages for Palestinian prisoners
The Indian constitution currently allows the country's 1.2 billion citizens to be governed by their own religious laws when it comes to marriage, divorce and property inheritance.
But Prime Minister Narendra Modi's government wants bring in a common civil code that it says will enhance national unity.
On Thursday the All India Muslim Personal Law Board said they would block any attempt to abolish Islamic family laws, which many Muslim women say discriminate against them.
"You can't impose a single ideology in India. Modi has triggered an internal war in India," Maulana Wali Rahmani, head of AIMPLB, told reporters at a press conference in New Delhi.
"A uniform civil code is not good for India, which has many cultures and religions. It will divide India," he said.
India's Law Commission has sought public feedback on a common law that would ban controversial practices such as polygamy and triple talaq divorce, under which a Muslim man can divorce his wife instantly with just three words.
The commission said the objective was to "address discrimination against vulnerable groups and harmonise various cultural practises".
Muslim personal law has long been a controversial issue in India.
Some Indian Muslim women have in recent years launched legal challenges to triple talaq, which they say discriminates against them and violates their human rights.
A case in the mid-1980s involving Muslim woman Shah Bano, who took her rejected demand for alimony to the Supreme Court, triggered debate across India over whether the court had authority over Muslim personal law.
The court upheld her right to alimony, but its verdict was reversed by a law passed by the then-Congress party government after Muslim groups reacted angrily.
Any attempt since then to bring a common civil code has proved deeply divisive in the officially secular but mainly Hindu country.
Negotiators have proposed a 40-day pause in the fighting and an exchange of hostages for Palestinian prisoners
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