The plot of the movie, adapted by Ron Howard from Dan Brown's worldwide best seller, makes the case that Jesus married Mary Magdalene and had children with her.
In India, the government Tuesday put a temporary hold on the movie's release because of complaints.
In South Korea, which has 13 million Protestants and 4.6 million Roman Catholics, a court ruled Tuesday that a Christian group's request for an injunction to block screenings lacked merit.
"As it is clear that the novel and movie are all fiction ... there is no probability that the movie can make viewers mistakenly believe the contents of the movie are facts," chief judge Song Jin-hyun said in his ruling.
The Christian Council of Korea, an umbrella group of 63 South Korean Protestant denominations, said it respected the ruling but would lead a boycott of the movie, which it said defiles the sanctity of Jesus Christ and distorts facts.
In Thailand, Christian groups demanded that government censors cut the film's final 15 minutes, fix subtitles that are supposedly disrespectful to Jesus and screen messages before and after the movie saying the content is fictional.
"If they are going to screen this, we asked that they cut out the conclusion of the movie that Jesus still has heirs alive today," said spokesman Manoch Jangmook, of the Evangelical Fellowship of Thailand.
The censor board has not yet replied to the request. The movie is scheduled to start running Thursday in Thai theaters.
In mostly Hindu India, which is also home to 18 million Roman Catholics, Joseph Dias, head of the Catholic Secular Forum, began a hunger strike in downtown Bombay and said other people were joining him.
"We want the movie to be banned," he said.
The film had been set for release in India on Friday and had already been cleared by the national censor board. But Information and Broadcasting Minister Priya Ranjan Dasmunshi said he put a temporary hold on the movie after receiving more than 200 complaints.
"We are a secular country. On any sensitive issue, we should take action after we examine every aspect," Dasmunshi told reporters.
In Athens, Greece, some 200 religious protesters, waving crucifixes and Greek flags, demonstrated Tuesday in protest of the film. The protesters — including Orthodox monks and nuns — later marched peacefully to parliament.
"All religions merit respect, so why don't they show respect in this case instead of attacking all that we hold sacred?" said Athanasios Papageorgiou, president of St. John the Theologian group in Peania, east of Athens.
"I've read the book. It's despicable," he added. "The Muslims for one cartoon burnt anything, so what should we do?"
Greece's powerful Orthodox Church has blasted the "ridiculous content" of the movie but stopped short of calling for its boycott.
Philippine censors approved an adult rating for the movie but stopped short of rating it "X" because "it does not constitute a clear, express or direct attack on the Catholic church or religion" and does not libel or defame any person.
The movie-review panel's chairwoman, Marissa Laguardia, told The Associated Press that the movie would be a "test of faith" for many people in the predominantly Roman Catholic Philippines.
"Those groups, like the conservatives who want it banned, maybe they can tell their friends, discourage their friends from watching it," she said. "But it has to be shown. Otherwise we will be the only country that will not show this film. Thirty-six countries have already reviewed this film and they have not banned it. So are we just out of the Stone Age?"
The National Council of Churches in Singapore, which also had requested a ban, planned lectures to refute aspects of the film and the book on which it is based. The censorship board gave the movie an NC16 rating, barring viewers under 16, arguing that "only a mature audience will be able to discern and differentiate between fact and fiction."
Also, while not planning a protest or boycott, members of the National Organization for Albinism and Hypopigmentation expressed unhappiness with the film's heavy, a monk-assassin, being an albino, as described in the book.
Michael McGowan, an albino who heads the organization, said "The Da Vinci Code" will be the 68th movie since 1960 to feature an evil albino.
The "Da Vinci" character "is just the latest in a long string," McGowan said. "The problem is there has been no balance. There are no realistic, sympathetic or heroic characters with albinism that you can find in movies or popular culture."
He said the group aims to use the movie's popularity to raise awareness about the realities of albinism. People with albinism have little or no pigmentation in their skin, eyes and hair.