(Adds further source, birthplace, comment)
By Lamine Chikhi and Marie-Louise Gumuchian
ALGIERS, Aug 30 (Muammar Gaddafi became a grandfather again on Tuesday when his daughter Aisha gave birth to a girl within hours of fleeing across Libya's desert border into Algeria, officials said.
Algerian officials highlighted the plight of the expectant mother in explaining a decision to give refuge to the fugitive Libyan ex-leader's wife and three of her children on Monday -- a move denounced by the country's new rulers as an act of aggression.
The child was born in Djanet, according to two Algerian official sources. An oasis deep in the Sahara, Djanet lies about 60 km (40 miles) from the Libyan frontier and 500 km southwest of Sabha, one of the last bastions of support for Aisha Gaddafi's 69-year-old father.
"Gaddafi's daughter gave birth to a girl today," a source close to the Algerian health ministry, who spoke on condition of anonymity, told Reuters. "This is all I can say."
Aisha Gaddafi, a lawyer in her mid-30s about whom little information can be confirmed, was on the very point of giving birth when the family appealed to cross the border, another Algerian source said. That humanitarian consideration was the main reason for them being allowed in, the source added.
Algeria's ambassador to the United Nations, Mourad Benmehidi, told the BBC that in the desert regions there was a "holy rule of hospitality."
Analysts say the government in Algiers is wary of popular unrest in other Arab states and fears its own Islamist enemies may find support in the new Libya.
However, a local newspaper in Algiers reported that Algeria would hand over Muammar Gaddafi to the International Criminal Court (ICC) if he himself entered the country. Another paper said part of the Libyan border would be closed.
NO HAVEN FOR GADDAFI
Gaddafi's wife Safia and sons Hannibal and Mohammed were also in the party given refuge. Libya's ruling council demanded them back for trial. But only Gaddafi himself, his son Saif al-Islam and a senior aide, who are both also in unaccounted for, are subject to an international arrest warrant for war crimes.
Gaddafi's only daughter who was not adopted, Aisha ran a charitable foundation and in 2004 joined a team of lawyers defending former Iraqi leader Saddam Hussein. There had been no public announcement that she was expecting a child.
Aisha largely stayed out of Libyan politics, but since the start of a revolt against her father's rule in February she appeared at pro-Gaddafi rallies and gave interviews in which she accused NATO of killing Libyan children.
Quoting Algerian sources, the Echorouk newspaper said on its website that President Abdelaziz Bouteflika had told government ministers at a cabinet meeting on Monday Algeria would respect international law on all matters related to the Libyan conflict.
"Should Gaddafi try to enter Algerian soil ... Algeria would arrest him and hand him over to the International Criminal Court in compliance with international agreements," the newspaper said.
It said the decision was not a reaction to the toppling of Gaddafi but was in accordance with the ICC's arrest warrants.
No one was immediately available from the government for comment.
In a separate report, Echorouk said Gaddafi's family would not be allowed to go to the capital Algiers.
Algeria's El Watan newspaper said the country was closing the southern part of its border with Libya. Quoting diplomatic sources, El Watan said an instruction had gone out to security services to close the southern part of the border with Libya because of the "precarious situation" there.
Algeria's border with Libya is hundreds of kilometers long and stretches through expanses of empty desert.
Algerian officials say they are concerned that Islamist militants have infiltrated Libya's National Transitional Council (NTC) and that al Qaeda's North African wing will exploit the chaos in Libya to acquire weapons and explosives.
The NTC has denied those charges and in turn accuses Algeria of siding with Gaddafi during Libya's civil war, something the Algerian authorities deny.
(Additional reporting by Joseph Nasr in Berlin; Writing by Christian Lowe and Alastair Macdonald in Tunis; Editing by Angus MacSwan)