Kumar, who had moved a divorce petition, expressed willingness in a court here to arrive at a settlement through mediation to which Chief Judicial Magistrate (CJM) Snehalatha gave her consent.
As the talks remained inconclusive with the two sides failing to reach agreement on certain sensitive issues, the CJM posted the case to April 12 for further proceedings.
Kumar was forced to resign from the Congress-led UDF Ministry on April 2 after Yamini lodged a police complaint alleging she had been a victim of domestic violence for the last 16 years, which marked a critical turn in the long-running family dispute.
She had also filed a petition in the CJM court yesterday seeking to book her husband under the Protection of Women from Domestic Violence Act and sought a compensation of Rs 20 crore from her husband.
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The court in its interim order directed Kumar not to take steps to dispose of the house in which Yamini and their children were residing or any household articles.
When the divorce case was taken up this morning, Kumar's counsel told the court that he was willing to go for mediation to settle the dispute, including the compensation sought by Yamini as part of their separation.
Kumar's exit from the ministry also marked a long-drawn rift with his father and Kerala Congress (B) supremo R Balakrishna Pillai, who wanted his son to be dropped from the cabinet on the ground that he ignored the party's interests.