"MP Civic poll results are gladdening. I thank people of MP for reposing their trust in BJP. I salute efforts of karyakartas (workers) and party leaders," Modi tweeted.
"Thank you very much for your continued support and faith. MP will continue to work under your dynamic leadership," Chief Minister Shivraj Singh Chouhan, who has been facing demands for his resignation over the scandal, tweeted.
The elections were held on August 12.
BJP registered victories in Morena, Ujjain, Harda, Chakghat in Rewa district, Bhainsdehi in Betul district, Kotar in Satna, Suwasara in Mandsaur and Vidisha municipal bodies.
A Congress and an Independent candidate were elected as President of municipalities in Sarangpur in Rajgarh district and Guhwara in Chhattarpur district respectively.
BJP had swept the civic polls in the state held earlier this year. Elections in the aforementioned 10 municipal bodies could not be held then due to various reasons.