ALGIERS, Algeria (AP) -- One day after fleeing Libya, Moammar Gadhafi's daughter gave birth to a baby girl in Algeria on Tuesday, the Algerian Health Ministry said.

An official with the ministry said that Aisha Gadhafi gave birth but provided no other information, including where that happened. The official was not authorized to be publicly named according to ministry rules.

Gadhafi's wife Safia, his sons Hannibal and Mohammed, and his daughter Aisha entered southern Algeria from the Libyan border Monday, the Algerian Foreign Ministry said. Algerian news reports had said Aisha's pregnancy was one reason for Algeria's controversial decision to take the family in.

Libya's rebel leadership demanded Tuesday that Algeria return Gadhafi's wife and children for trial, accusing Algeria of an "aggressive act." The departure of Gadhafi's family was one of the strongest signs yet that he has lost his grip on Libya after 42 years in power.

Aisha Gadhafi, in her mid-30s, is a lawyer who helped in the defense of toppled Iraqi dictator Saddam Hussein in the trial that led to his hanging.

After Libyan rebels advanced on Tripoli last week, her home was among those exposed to looting.

She lived in a two-story mansion with an indoor pool and sauna, where DVDs included action and mystery films, but also one on getting back in shape after childbirth. A large play room was strewn with toys, party hats and streamers were in a pile in an entrance hall, and her library contained a number of children's books.

Earlier Tuesday, an Algerian newspaper reported that the government has moved to partially close Algeria's southeastern border with Libya after members of Gadhafi's family fled across it. The El-Watan daily cites unidentified diplomatic officials Tuesday as saying security forces have been deployed to shut the border.

The Foreign Ministry and the Defense Ministry would not comment on the newspaper report.

Separately, the Algerian daily Echourouk, citing unidentified officials, said 31 people connected with the Libyan dictator's family had entered Algeria - including his grandchildren and servants. It said Aisha was in critical condition and close to giving birth.

(This version CORRECTS Corrects that birthplace was not announced, updates with Algerian border reportedly closed, adds background on Aisha Gadhafi.)