ABIDJAN (AFP) - Ivory Coast was in political turmoil Monday after rivals for the presidency each named their own prime ministers while international mediators tried to settle the standoff amid fears of civil war. Incumbent Laurent Gbagbo and his old rival Alassane Ouattara have both sworn themselves in as president and each pressed on as if he was in charge despite mediation attempts by South Africas former president Thabo Mbeki. Gbagbo, 65, has defied international calls to cede power after the UN recognised Ouattara as the winner of the Nov 28 runoff vote, which was supposed to stabilise the country but has been marred by deadly violence. But after Mbeki, sent by the 53-member African Union (AU), held emergency talks with the two on Sunday, Ouattara upped the ante. He called on the mediator to demand Gbagbo quit, as his own allies declared they had formed a new government. Gbagbo later issued a rival presidential decreed naming Gilbert Marie Ngbo Ake as his new prime minister. An AU source said Mbeki stayed the night in Abidjan and further meetings were likely on Monday morning. Hundreds of people fearing violence meanwhile began crossing west from parts of Ivory Coast controlled by Ouattaras supporters into neighbouring Liberia, an official there said. Despite an earlier order by Gbagbo for Ivory Coasts borders to be sealed, there are more than 300 Ivorians who have already crossed the borders into Liberia, the top Liberian official for refugees, Saah Nyumah, told AFP. Nyumah warned of impending food shortages if the numbers increase. Later Sunday, the army officially reopened Ivory Coasts borders, but said security would be reinforced. Ouattara told reporters after talks with Mbeki: I asked him to ask Laurent Gbagbo not to hang onto power... to quit power, as you should when you lose an election. The political crisis is obviously very serious, Mbeki told reporters. Among other things, its important not to have violence, not to return to war and so on, to find a peaceful solution. Ivory Coast was split in two between north and south by a civil war in 2002 and 2003. The election was supposed to end a decade of conflict in the country, which was once the most prosperous in west Africa. But it was plunged into turmoil when the Constitutional Council invalidated results announced by the electoral commission that gave Ouattara a win with 54 percent of the vote, proclaiming Gbagbo the winner instead with 51.45 percent. The United Nations certified the results showing Ouattara as the winner, but Gbagbos high court allies overturned them by annulling allegedly rigged ballots in parts of the north, his rivals stronghold. At least 17 people have been killed in election-related clashes since last week and the AU warned in a statement at the weekend that the standoff could erupt into a crisis of incalculable consequences. It called on Gbagbo to recognise Ouattara as the winner, but the incumbent, in office since 2000, has defied all calls to cede power, telling outsiders to mind their own business. I am charged with defending our sovereignty and I will not negotiate on that, he said on Saturday after being sworn in. Former rebel leader and incumbent prime minister Guillaume Soro on Sunday read out to reporters a list of 13 Ouattara allies named in a new government, including himself as premier and defence minister. There must be a transition of power, Soro told Frances Europe 1 radio on Monday. Theres no question of dividing Ivory Coast. Gbagbo in turn appointed as his premier Ake, an economist who is dean of Abidjans main university. State television has broadcast pictures of military leaders apparently pledging allegiance to Gbagbo. Soldiers were deployed around Abidjan, while armoured vehicles from a UN peacekeeping force guarded the hotel housing Ouattaras campaign base.