* Ouattara says receives Mbeki in role as president
* Mbeki canvassing "all points of view"
* Rebel commander says forces won't wait long
(Adds Gbagbo names prime minister, paragraph 5)
By Loucoumane Coulibaly and David Lewis
ABIDJAN, Dec 5 (Reuters) - Presidential claimant Alassane Ouattara said on Sunday that incumbent Laurent Gbagbo must step down after a disputed poll in Ivory Coast, and he named a rival government as African mediators tried to resolve the stalemate.
The Nov. 28 election was aimed at reuniting the West African nation, split after a 2002-3 civil war, but both Gbagbo and Ouattara have claimed victory and taken presidential oaths.
Gbagbo was sworn in as president on Saturday even though the electoral commission declared Ouattara the winner, according to provisional results giving him a 10 percent lead that were ratified by the United Nations.
Ivory Coast's military said it would re-open its land, air and sea borders from Monday at 6 a.m. (0600), after they were sealed during a tense wait for election results. It was unclear why the military decided to reopen the borders at this point.
State TV announced shortly before midnight that Gbagbo, a former history professor, had named the president of Abidjan's Cocody university, Gilbert Ake, to be his prime minister.
Ouattara's comments after talks with Thabo Mbeki, the former South African president leading the mediation effort, showed he was in no mood for compromise after securing endorsements from the United Nations, neighbours and others.
"I told President Mbeki I am the president of Ivory Coast and it is in that capacity that I am receiving him, and asking him to urge Mr Gbagbo to ... step down as he should after losing an election," Ouattara said after talks in a U.N.-guarded hotel.
He later named a government including Gbagbo's former premier Guillaume Soro as prime minister and defence minister. Soro had resigned from Gbagbo's administration in protest at his proclaimed election victory, saying in a statement: "Ouattara clearly won."
Ouattara also named Gbagbo's former finance minister, Charles Koffi Dibby, in his cabinet. Dibby, a technocrat who has been praised for his handling of the economy and debt negotiations, was unavailable to confirm he had switched sides.
Mbeki told reporters only that the talks with Ouattara had been positive and that the African Union considered the situation in the world's top cocoa grower very serious.
"We want to hear all points of view on this matter before we can make any recommendations," he said.
In the northern town of Bouake, the stronghold of rebels opposed to Gbagbo, tens of thousands of Ouattara supporters demonstrated outside the local headquarters of the U.N. peacekeeping mission, whose envoy has said Ouattara won the poll, demanding that Gbagbo step down.
"ADO President!" chanted his supporters, referring to their man by his initials. The mood of the demonstration was calm.
Hundreds of thousands of votes in Bouake and other northern towns were scrapped by the Constitutional Council, headed by a Gbagbo ally, to reverse Ouattara's win in provisional results. That led the opposition, U.N. and foreign powers to cry foul.
"A situation like Rwanda or Kenya would be a nightmare, which we are working tirelessly to avoid," South Africa's envoy to Ivory Coast, Zodwa Lallie, told Reuters.
A disputed result in Kenya's election in 2007 degenerated into ethnic bloodshed that killed at least 1,300 people.
Gbagbo has controlled the country for a decade but now faces isolation and possible sanctions. His proclaimed win was rejected by the United Nations, the United States, France, the European Union, the African Union and West African bloc ECOWAS.
The Constitutional Council cited intimidation by rebels who run pro-Ouattara northern areas, but the U.N. peacekeeping envoy to Ivory Coast, Y.J. Choi, certified the provisional result. He received copies of the count from almost every polling station.
He said that even if all the fraud allegations were true, they still could not have changed the outcome.
"He (Ouattara) can call himself president but there still needs to be a way for the ruling party to accept defeat," said one diplomat watching events in Abidjan. "In terms of exercising executive power, he is a long way from doing that."
The crisis in Ivory Coast, once West Africa's brightest economic star, has sent cocoa futures up to two-week highs and forced up the risk premium on the country's $2.3 billion Eurobond. It is currently yielding 11.67 percent, from below 10 percent after the first election round.
New Forces rebel commander Cherif Ousmane said his followers would "not rest for long without doing something" about Gbagbo if he continues to hold onto power.
Additional reporting by Tim Cocks and Ange Aboa; writing by Mark John; editing by Michael Roddy