In India on Wednesday about 2,000 Roman Catholics marched through Mumbai, many carrying placards saying: "Stop hurting our faith."
In the Philippines, where more than 80% of the population is Catholic, a government official called for the film to be banned in the country, describing it as blasphemous.
"I think we should do everything not to allow it to be shown," Eduardo Ermita, executive secretary to the president, said on Wednesday.
The Vatican has also condemned the film, and Cardinal Francis Arinze urged Christians to take legal action to protect their faith from "those who blaspheme Christ".
Meanwhile in Jordan, a Muslim country, the Council of Churches called for the film to be banned.
Catholic leaders in Greece and Austria have also condemned the film.
The film is based on the eponymous novel by Dan Brown, an American author. It contains the premise that Jesus was married to Mary Magdalene, one of his followers, with whom he had children.
The film and novel have been criticised by Opus Dei, a conservative Catholic organisation that features heavily in the novel and which claims it has been unfairly depicted.
"This is a work of fiction ... it's not theology, it's not history"
Ron Howard, film director
"Those who do further research and exercise critical judgment will discover that assertions made in The Da Vinci Code ... lack support among reputable scholars," the group said in a statement.
It has also demanded that the film carry a disclaimer before any film screening, saying that the events it depicts are fictional.
However, Ron Howard, the film's director, rejected the demand and defended the film's subject matter.
"This is a work of fiction ... it's not theology, it's not history. Spy thrillers don't start off with disclaimers," he told the Los Angeles Times newspaper.
The Da Vinci Code - Sony Pictures