Brad Pitt and a pregnant Angelina Jolie, who are awaiting the "imminent arrival" of their first child, want their stay in Namibia to be as private as possible.
Foreign journalists wanting to cover the birth must have written permission from the Hollywood stars to enter the country, and anyone who doesn't have their OK could be expelled, the Namibian government has said.
Pitt, 42, sent an e-mail to the Cannes Film Festival in the south of France on Tuesday, saying he couldn't attend the screening of his new film, "Babel," due to "the imminent arrival of the newest addition to our family."
Since Pitt and Jolie, 30, and her two young children, Maddox and Zahara, arrived in the sleepy coastal town of Walvis Bay last month, they have been shielded by their own bodyguards and Namibian police at the luxury Burning Shores resort hotel.
Maddox and Zahara have legally had their surname changed to Jolie-Pitt.
Last month, the couple's security chief gave a local journalist a statement signed by Pitt and Jolie asking that they be left alone.
Photographers have gotten a few shots, but for the most part, they have had to settle for photos of large, green barriers set up on the beach to block the view of prying lenses.
Samuel Nuuyoma, the governor of the Namibian province where the family is staying, has been quoted as saying he would visit the hospital and name the baby.
"No. No. That's absolutely not true," Nuuyoma, who has met the couple, told The Associated Press on Wednesday.
"I never said such a thing. Never in history," he said, abruptly ending the phone conversation.
Namibians are aware that Pitt and Jolie's presence has increased the international profile of the country's brilliant scenery and plentiful wildlife.
An informal poll by Namibian station Radio Wave determined that listeners were evenly divided on whether the day Jolie gives birth should be declared a national holiday, according to the station's Web site.
Meanwhile, Jolie, who is a goodwill ambassador for the U.N. High Commissioner for Refugees, has attracted the attention of Botswana's beleaguered bushmen of the Kalahari desert.
"Dear Ms. Jolie, WE, First People of the Kalahari, have heard that you are in Namibia, near us in Botswana, for your holidays. We also heard you are pregnant and want to wish you our blessings," said a letter printed in Wednesday's edition of the Namibian newspaper.
The letter went on to seek Jolie's help resisting the Botswanan government's campaign to evict the bushmen from the Kalahari Game Reserve and move them to resettlement camps, "where our lives have totally changed and we are about to lose our culture."
Namibia, a country half the size of Alaska, is rich in diamonds and strategic metals, but most of its 1.8 million people are poor.