Dzasokhov's term expires in January 2006.
Kozak arrived in North Ossetian capital Vladikavkaz on Tuesday to meet with Dzasokhov and discuss candidacies of his successor.
Among them are speaker of the North Ossetian parliament Taimuraz Mansurov, First Deputy Prime Minister Alexander Merkulov and mayor of Vladikavkaz Kazbek Pagiyev. The latter withdrew his candidacy at once.
According to Kozak, President Vladimir Putin will consider the candidacies.
Dzasokhov explained his resignation with the decision to make way for the younger generation.
"I am making a precedent. When everyone strives for prolonging his term I will reduce it," Dzasokhov said.
It was not a hasty decision, he added. "My term expires next year. I would not run for another term," he said.
However, the North Ossetian president does not intend to give up politics.
"Politics is a profession. I have been in politics for many years" and cannot change it now, Dzasokhov said.
I hope to be useful "without any ambitions and claims for top posts, I will help the country and Russian president without losing links with my native republic," he added.
Speaking about his feelings, Dzasokhov said: "Love for North Ossetia is my main feeling. I chose this destiny myself when I came here from Moscow eight years ago. I am convinced it was the right decision."
The question of Dzasokhov's resignation was raised for the first time after the Beslan tragedy in North Ossetia on September 1-3, 2004. Terrorists took 1,100 people hostage at Beslan's school No. 1. A total of 335 people died and some 400 were wounded.
Then Dzasokhov said that his resignation would be regarded as an attempt to shrink away from responsibility.
