Pitt, a pregnant Jolie and their children Zahara and Maddox taking a holiday under tight security at an exclusive African resort as the due date nears, and the Namibian government has threatened to expel anyone trying to cover the birth without permission.
Interest has heightened in recent weeks, as the baby had been expected in mid-May. Pitt sent an e-mail to the Cannes Film Festival, read to reporters at the French resort Tuesday, saying he was unable to attend this year's event because of his third child's "imminent arrival."
Photographers on the hunt in Namibia have gotten a few shots, but for the most part had to settle for shots of large, green barriers set up on the beach to shield the family from prying lenses. Journalists desperate for news have resorted to quoting Namibian government officials — not always accurately, apparently.
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," Samuel Nuuyoma, who has met the couple, told The Associated Press Wednesday.
"I never said such a thing. Never in history," he said, abruptly ending the phone conversation.
Sine the co-stars of "Mr & Mrs. Smith" and their entourage arrived in the sleepy coastal town of Walvis Bay in April, they have been shielded from reporters by their own body guards and Namibian police at the luxury Burning Shore hotel in an area where Namibia's famed desert sand dunes descend spectacularly to the sea.
Namibians are well aware Pitt and Jolie have increased the international profile of the country's brilliant scenery and plentiful wildlife. Namibian station Radio Wave conducted a far from scientific poll and determined listeners were evenly divided on whether the day Jolie gives birth should be declared a national holiday, according to the station's Web site.
Holidays aside, Namibians have championed their celebrity visitors' right to privacy.
The government has said foreign journalists wanting to cover the birth must have written permission from Pitt and Jolie to enter the country.
South Africa's Sunday Times said last month its own photographer and three French photographers were ordered to leave Namibia or face arrest.
"This lady is expecting," Namibian Prime Minister Nahas Angula told the paper at the time. "You guys are harassing her. Why don't you allow her some privacy? Harassment is not allowed in Namibia."
The couple's security chief last month gave a local journalist a statement appealing for privacy.
"We love Africa and to be here in Namibia with our family is very special for us," it said. "To the local people who have been so kind and gracious, thank you for making us feel at home."
"As for the press, we kindly ask for privacy so that we can enjoy this beautiful country with our children." It was signed Angelina Jolie and Brad Pitt.
Jolie, goodwill ambassador for the U.N. refugee agency, has continued with her charitable work while in Namibia, visiting school projects and community centers involved in education. She took part in a telephone conference call with reporters to publicize efforts to raise money to provide an education for 100 million children in poor nations who are not now in school.
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.
Jolie has traveled to Africa frequently to shoot films and as a goodwill ambassador. She has called the continent one of hope and possibility, and she adopted her daughter, Zahara, from Ethiopia last year. She adopted Maddox in 2002 in Cambodia, where she filmed "Lara Croft: Tomb Raider." Both children have since also been adopted by Pitt and have legally had their surname changed to Jolie-Pitt.
Jolie's reputation 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."