Afghanistan's two presidential rivals have failed to come to a power-sharing deal in their long-lasting talks, despite another meeting.

Both presidential candidates claim to have won the run-off June 14 election, causing a political stalemate and raising ethnic tensions as US-led NATO combat troops withdraw after 13 years of fighting against Taliban.

Abdullah Abdullah, a former foreign minister, who has threatened to form a parallel government various times before, was expected to hold a news conference later on Monday to reveal his current position.

According to a preliminary count, Ghani, a former finance minister, took the second round, but both sides have alleged election fraud.

Al Jazeera’s Jennifer Glasse, reporting from Kabul, said the Ghani camp did not take Abdullah’s ultimatum to form a parallel government seriously.

"They say even if Abdullah's camp forms a parallel government, it does not mean anything. 'Who are they going to rule?' Ghani supporters say," she said.

She said the Ghani camp wanted to see what would come out of the UN audit in the coming weeks.

The UN, which is currently responsible of audit of the votes due to fraud allegations, has said results of an audit into the polls should be finalised by September 10, with the delayed inauguration of President Hamid Karzai's successor scheduled to be held soon after.

US President Barack Obama on Sunday urged Abdullah and Ghani to come to an agreement on a national unity government to end the crisis over the vote.

In telephone calls with both candidates, Obama "emphasised the importance of concluding a deal on the national unity government as soon as possible in the interest of shoring up international support for Afghanistan and preserving Afghan stability", the White House said.

"The president reaffirmed the US' commitment to support Afghanistan, its people, and the president and chief executive, should the agreement be formalised, in their efforts to form a new unity government," it said.