BNP Chairperson Khaleda Zia has demanded arrest of those involved in the attack while Mirza Fakhrul described it as 'an attack on democracy'.
Hasan Mahmud, the Awami League's local MP, has denied the allegation that his supporters carried out the attack.
The ruling party's General Secretary Obaidul Quader has condemned the attack and promised a fair investigation.
He said both he and Fakhrul have been injured in the attack.
The seven-member delegation started from Chittagong in the morning for Rangamati's Kaptai. They were scheduled to board a vessel from there for Rangamati town.
"As soon as we reached Rangunia's Ichhakhali, men armed with iron rods and sharp weapons attacked our convoy. They have completely damaged our cars," said Amir Khosru, a member of BNP's policymaking National Standing Committee.
Later in the day, the BNP leaders held a press conference where Fakhrul said the attack targeted those who are vocal against the ‘misdeeds’ of the government.
“The Awami League has exposed its true nature. They speak of democracy but do not believe in it,” Fakhrul told reporters at the Chittagong Press Club.
Mahmud, the local MP and the ruling party's publication secretary, alleged that the car carrying the BNP secretary general hit two persons in Ichhakhali.
Later in the night, Mahmud sent photographs to bdnews24.com where he is seen clad like a day-labourer and carrying a basketful of soil as part of the inauguration of the development work on a road in Chittagong’s Rangunia in the afternoon.
“The Awami League leaders and activists are repairing the roads damaged in natural calamity in Rangunia municipality,” he said.
The attack prompted the BNP to call nationwide protests for Monday.
BNP chief Khaleda condemned the government’s failure to make any arrest after the attacks.
“By contrast, our men get sued and arrested immediately if something happens, despite having no involvement,” she said at an Iftar party on Sunday.
“They must be arrested, punished, jailed. I want justice for this.”
Awami League General Secretary Quader said the attackers will be brought to justice.
"The incident shouldn't have happened. Whoever did this, it was wrong," he told reporters.
The road transport minister also said he has asked the police to find the culprits following a neutral investigation.