The church is seeking to challenge a lower court's ruling last October that sides with the Muslim-majority country's government forbidding non-Muslims from using the Arabic word "Allah" in the local Malay language.
A seven-judge bench in Malaysia's Federal Court is expected to decide on Wednesday whether it will allow a full hearing of the case or whether the lower court's verdict stands.
Some 500 Muslims gathered outside the court complex in the administrative capital of Putrajaya as the case began, chanting "Allahu Akbar" or "God is great" and holding banners that read: "Want to use 'Allah', join Islam. Don't be ill-mannered".
"Allah cannot be used by outsiders or Christians. People now may know the difference but our children will not know," Rosli Ani, a representative of a Muslim NGO known as Per3, said.
Father Lawrence Andrew, the editor of the Catholic newspaper Herald, which launched the case, said Christians across Malaysia were fasting and praying for a favourable verdict.
Wednesday is Ash Wednesday, the beginning of the holy period of Lent, which precedes Easter and during which many Christians fast.
An appeals court in October barred the Herald from using "Allah" in its Malay-language edition, overturning a lower court's 2009 ruling in favour of the church.
The church argues "Allah" has been used for centuries in Malay-language Bibles and other literature to refer to "God" outside of Islam.
But authorities say using "Allah" in non-Muslim literature could confuse Muslims and entice them to convert, a crime in Malaysia.
The dispute first erupted in 2007 when the Home Ministry threatened to revoke the Herald's publishing permit for using the word.
Amid the row, two petrol bombs were thrown at a Malaysian church in late January, causing minor damage but triggering memories of a wave of such attacks on places of worship -- mostly churches -- four years ago during an earlier bout of divisions over the case.
Malaysia has largely avoided overt religious conflict in recent decades, but tensions have slowly risen along with what many see as increasing Islamisation of the Southeast Asian nation.
Muslim ethnic Malays make up more than 60 percent of the country's 28 million people, which also includes sizeable Chinese, Indian and other minorities. About 2.6 million people in Malaysia are Christians.
The World Council of Churches recently said it was "deeply concerned by recent developments (including the October court ruling) that jeopardise these fundamental values (of freedom of religion and belief) and the long history of multi-religious co-existence in Malaysia".