The leaders slammed Swamy, saying his comments on the Kartarpur corridor had hurt sentiments of the Sikhs.
In a joint press statement, Ministers Sukhjinder Singh Randhawa and Bharat Bhushan Ashu, besides legislators, said the BJP-ally Shiromani Akali Dal (SAD) must clear their stand on the issue.
"The entire Punjab, especially the Sikh circle, knows it too well that the Badal family loves to cling to power rather than working for Sikh interests," they said.
The silence of the SAD on various issues, including the opposition to the corridor by a BJP leader, "proved that it was hand in glove with the BJP in this sin", they said.
"It was part of a deep-rooted conspiracy that Swamy gave this statement (on Saturday) in Chandigarh. Now, the cat has come out of the bag and the Punjab BJP leadership must clarify their position as to whether they are in agreement with the statement of their party leader or not," they said.
Swamy had on Saturday said the work on the Kartarpur corridor should be stopped in the interest of the nation.
Clarifying the party's stand on the issue, state BJP President Shwait Malik told the media that this was Swamy's personal opinion.
Reacting to the statement by the Congress leaders, Akali Dal national spokesperson Manjinder Singh Sirsa blamed Chief Minister Amarinder Singh for planting the seeds of doubt about the Kartarpur corridor.
"It was always Congress which hurt the goodwill gesture done for Sikhs," Sirsa, who is the Delhi Sikh Gurdwara Committee President, tweeted.
"Sukhjinder Randhawa, Bharat Bhushan Ashu & other Congress leaders need to come clean on their stand on Kartarpur corridor," he added.
Last month, Pakistan agreed in principle to allow visa-free, year-long travel to the Kartarpur Sahib Gurdwara for Indian passport holders and Overseas Citizenship of India (OCI) card holders via the upcoming 4.2-km-long corridor, which is scheduled to be opened by October 31, a week before the celebrations to mark the 550th birth anniversary of Guru Nanak Dev.
Currently, devotees from the Indian side can pay obeisance by seeing the white-coloured Kartarpur Sahib Gurdwara located in Pakistan through binoculars.
Pakistan's doors are open to Indian Sikh pilgrims visiting Darbar Sahib Kartarpur in connection with the 550th birth anniversary of Guru Nanak, irrespective of Islamabad's ties with New Delhi, said Firdous Ashiq Awan, the Special Assistant on Information and Broadcasting to the Pakistan Prime Minister.
Addressing a press conference in Lahore on Saturday, she rejected rumours that Pakistan has stalled work on the Kartarpur corridor after straining of relations with India over New Delhi's move to revoke the special status of Jammu and Kashmir, Radio Pakistan reported.
( With inputs from IANS )