"I went to see him (Keita) to congratulate him and wish him good luck for Mali," AFP quoted Cisse as saying on Monday.
No official results have yet been released, but the electoral and security sources said Keita, also known as IBK, had pulled ahead with two-thirds of votes counted.
"With nearly two-thirds of the ballots counted, IBK is well ahead," said a source close to Mali's election commission, which helped organize the polls.
Earlier on Monday, Cisse complained that the vote had been marred by fraud and intimidation. However, international and local observers said that despite small irregularities, the process had been credible.
"This election, from a democratic standards point of view, is a success," said the head of a European Union observer mission, Louis Michel.
"It is an election that allows Mali now to start finishing the process that it has begun: the return to a normal democracy," he said.
Malians went to the polls on Sunday to choose between Keita, 68 and Cisse, 63.
Keita had won 40 percent of the votes in the first round.
The election, the first since 2007, came following last year’s coup that ignited a rebel insurgency.
Chaos broke out in Mali after President Amadou Toumani Toure was toppled in a military coup on March 22, 2012. The coup leaders said they mounted the coup in response to the government's inability to contain the Tuareg rebellion in the north of the country, which had been going on for two months.
However, in the wake of the coup d’état, the Tuareg rebels took control of the entire northern desert region, but the Ansar Dine extremists then pushed them aside and took control of the region, which is larger than France or Texas.
In January 2013, France launched a war in the West African country under the pretext of driving out militants occupying the north.
Analysts believe that Mali’s untapped resources, including oil, gold, and uranium, are behind the French military campaign.