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.