"I thank the emir for accepting my resignation and understanding its reasons," Ajmi, who also holds the justice portfolio, said on his Twitter account without explaining the reasons.
Local media says he has quit for health reasons.
This is the second time in about five weeks that Ajmi says he has resigned.
In early April he submitted his resignation following accusations by a US official that he had links with Jihadists in Syria but it was turned down by Emir Sheikh Sabah al-Ahmad Al-Sabah.
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His appointment as minister in January was a "step in the wrong direction", Cohen said in a lecture in the United States, parts of which were carried by the Kuwaiti press in March.
A statement released after a March 31 cabinet meeting said ministers had followed Cohen's comments "with great attention and displeasure".
Ajmi acknowledged he had taken part in fund-raising campaigns for Syria, but insisted they had been for humanitarian purposes and not for Syria's Al-Qaeda affiliate Al-Nusra Front as alleged by Cohen.