Kunal Ghosh, an elected representative of the Trinamool camp, says his vehicle was targeted by masked men on motorcycles in Beleghata on Sunday.
The Saturday incident in Hooghly saw a mob stop the car and hurl eggs, forcing Ghosh to retreat to Kolkata.
Ghosh claims the second assault involved a revolver and hammer, suggesting a lethal intent.
Abhishek Banerjee, a Lok Sabha MP, condemned the attacks and demanded that the Governor and police investigate.
The assaults reflect a broader wave of violence against Trinamool leaders since the May assembly elections, with the party blaming the BJP.
Police have launched an inquiry and are seeking the identities of the perpetrators.