Kalvitis, the country's longest serving prime minister, was criticised for failing to respect the rule of law and overestimating his power to hire and fire officials.
The anti-corruption chief denied any misdeeds and the prime minister was eventually forced to reinstate him.
Kalvitis announced on November 7 that he would resign, after coming under further pressure from Zatlers due to a number of ministerial resignations.
Four ministers left the government or were dismissed following two large street protests over the anti-corruption chief's sacking, intensifying the centre-right government's problems.
Kalvitis, who became prime minister in December 2004, will act as caretaker prime minister of the Baltic state until his successor is appointed in the coming weeks.
Zatlers said on Wednesday that he will hold talks with three candidates, including Ivars Godmanis, the interior minister and Valdis Dombrovskis, the former finance minister and a member of the opposition, for nomination to form a new government.
He said that he was seeking a stable government to deal with rising inflation, which in October grew at an annual rate of 13.2 per cent, the highest in the European Union..
"I do not want to rush the process, but I cannot delay it either," Zatlers said.
Kalvitis' People's Party heads the outgoing ruling four-party coalition. It has yet to name a candidate to replace Kalvitis.
He told the "900 Seconds" news programme that he would not be a minister in the next government.
But the new coalition is likely to be made up of the same parties that control 56 seats in the 100-member parliament.