State Parliamentary Affairs Minister Partha Chatterjee said 10 Trinamool Congress activists, including the party's former legislator Arabul Islam, were injured.
The CPI-M said 27 of its cadres were seriously hurt in the clashes in Bhangar, about 30 km from Kolkata.
A large number of vehicles were reportedly torched.
The Left Front apprised Governor M.K. Narayanan of the "lawlessness" and the government's "inhuman" attitude.
State Congress chief Pradip Bhattacharya said his party was "extremely worried" over the deteriorating law and order and it would ask the union home ministry to send a special team to assess the situation.
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South 24-Parganas Superintendent of Police Pravin Tripathi told IANS that there was a law and order issue but he did not have "details".
Chief Secretary Sanjay Mitra said he was awaiting a written report from the administration. "An inquiry is on. Around a dozen people have been arrested," he said.
Chatterjee alleged that CPI-M activists, who were on their way in a convoy of cars to attend a demonstration, attacked Trinamool Congress workers with firearms.
He said that Trinamool Congress workers would take to the streets everyday after 6 p.m. Jan 10-18 to protest the "conspiracy" by the CPI-M, the Congress and two news channels to incite the public and create "lawlessness".
He alleged that CPI-M cadres attacked Arabul Islam. "Arabul has been admitted to a nursing home. Ten of our workers are injured," Chatterjee said.
Sports and Transport Minister Madan Mitra said the CPI-M was facing a "people's revolt".
"It is not that the Trinamool Congress is fighting the CPI-M. But representatives of the party can be part of the people," Mitra said.
Bhangar has become politically volatile since last week over clashes between the rival parties seeking to capture political turf ahead of the coming panchayat polls in the state.
Earlier a party office each of the CPI-M and Trinamool Congress were damaged and set on fire, respectively. When CPI-M legislator Abdur Rezzak Mollah went to the area Sunday, he was allegedly attacked by Trinamool Congress workers, led by Arabul Islam.
Mollah has been admitted to a private hospital with multiple injuries, and the incident has triggered a political uproar.
The Left Front had organised a demonstration in district headquarters Alipore condemning the attack on Mollah and demanding the arrest of Arabul Islam and others for the attack.
Arabul alleged that his car came under fire from the convoy carrying CPI-M workers.
"I have chest and leg injuries. When they started firing, I fell under the car. They continued to fire. Then my workers rescued me," said Arabul.
The Left front claimed 27 of its workers sustained injuries at Bamanghata when the vehicles carrying them to Alipore came under fire from a mob of Trinamool Congress supporters.
"Arabul spearheaded the attack with firearms. Twenty cars in the convoy were damaged. Thirteen of them were torched. Five of the injured have been hospitalised. Three have bullet injuries and one of them is very critical," said leader of opposition Surjya Kanta Mishra, who led a Left Front delegation to Narayanan at Raj Bhavan.
Mishra said Mollah, who has been an MLA for four decades, has fracture of the first lumber vertebra (spine).
Narayanan told the delegation that he would look into the issue.
Earlier in the day, the Left Front held a march in south Kolkata.
Left Front chairman Biman Bose told reporters that a statewide "condemnation day" will be observed Wednesday in protest against Tuesday's attacks.