Communists Party of India-Marxist (CPI-M) legislator Sudhan Das told the assembly that after the BJP-IPFT alliance attained majority in the February assembly polls, Left leaders and members are being attacked by the ruling parties, resulting in the resignations.
In reply, Mr Varma said, "Around 2,133 seats of three-tier local bodies - Zilla Parishad, Panchayat Samity and Gram Panchayat - were lying vacant.
"No specific complaint was submitted to me that any elected representative of these three local bodies has resigned following any intimidation," Mr Varma said in the house, which witnessed chaos and heated arguments on the issue.
Mr Das said, "Chief Minister Biplab Kumar Deb and other ministers are aware about some of the specific threats and intimidation to the elected representatives.
He said that there was no state in India where elected representatives of local bodies were forced to resign after the political change over of governance.
Meanwhile, the BJP-IPFT government on Tuesday introduced a bill in the assembly to provide an alternative mechanism for payments from the Gram Panchayat funds for completed works.
"All orders for payment from the Gram Panchayat Fund shall be signed jointly by the in-charge Panchayat Secretaries and and Block Development Officers concerned, till the time the new Pradhan or Upa-Pradhan are elected through due legal process, so that the development works are not hampered," said Mr Varma, who is in charge of Rural Development (Panchayat) Department.
Follow NDTV for latest election news and live coverage of assembly elections 2019 in Maharashtra and Haryana.
Subscribe to our YouTube channel, like us on Facebook or follow us on Twitter and Instagram for latest news and live news updates.