Over 500 Congress workers also protested against the comment of state Governor (Acting) P B Acharya at a public meeting.
The party staged a dharna in front of the Raj Bhavan to demand Swaraj's resignation for her "dubious role" in managing United Kingdom visa for former IPL chief Lalit Modi.
In a memorandum to President Pranab Mukherjee submitted through Kamrup (Metro) Deputy Commissioner, Assam PCC said "Lalit Modi is badly wanted by the Enforcement Directorate,has made London his base and has avoided coming to India where there is a look out notice for him for misappropriation of funds in the T20 Cricket Tournament".
"This is a gross violation of Indo-UK bilateral relations and serious breach of trust in discharging duties by a responsible union minister which has tarnished the reputation of our country in the eye of the world", the APCC claimed.
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It urged the president to take immediate steps for removing Swaraj from office in order to uphold the prestige and interest of the country.
"We request you to consider to exercise your discretionary powers to direct the Union Government to take cognizance of the matter and investigate the serious matter of receiving illegal gratification by Dushyant Singh.
"The very party that coined the much hyped 'ache din' promise to the people of the country had instead worked overtime to fill up their coffers and their corrupt corporate friends from ill-gotten wealth foregoing its obligations to the common people of the nation", the memorandum charged.