The Palins said that Bristol, who was named for Bristol Bay, the salmon fishery, would marry a man they identified only as Levi, later confirmed to be Levi Johnston, a Wasilla resident. “Bristol and the young man she will marry are going to realize very quickly the difficulties of raising a child, which is why they will have the love and support of our entire family,” the statement said.

The Palins’ statement arrived after a flurry of rumors had made their way through the Internet over the weekend, growing and blooming, it seemed, by the minute.

Some claimed that Ms. Palin had not actually given birth to Trig, but that Bristol had, and that the family had covered it up. Various Web sites posted photographs of Ms. Palin in the months leading up to his birth this year, and debated whether her physique might have been too trim for her stage of pregnancy. The McCain campaign said Ms. Palin announced Bristol’s pregnancy to stop the swirl of rumors.

Ms. Palin’s own pregnancy took Alaska by surprise this year. Even those who worked for her in the governor’s office said they were surprised. Her announcement, in March, was reported in The Anchorage Daily News, which noted at the time that Ms. Palin “simply doesn’t look pregnant.”

Friends said that Ms. Palin, a conservative Protestant and a member since 2006 of Feminists for Life, an anti-abortion group, knew when she was pregnant with Trig (said to be a Norse name for strength) that he had Down syndrome  a fact that has, in some ways, sealed Ms. Palin’s support among anti-abortion advocates and others.

“The governor sent a personal letter out to her friends and let us all know she was pregnant and that Trig would be a special baby in many ways,” said Kristan Cole, one of Ms. Palin’s closest friends in Wasilla, the town where Ms. Palin had served as mayor.

In 2002, when Ms. Palin was completing her second and final term as mayor, her husband’s stepmother, Faye Palin, began campaigning to succeed her. Faye Palin, though, favored abortion rights, people who recalled the race said, and Ms. Palin sided instead with Dianne M. Keller, a City Council member who won the race and remains mayor there today.