The demand by Swaraj came when Congress President Sonia Gandhi called her last night in a bid to break the logjam in Parliament over the CAG report on coal block allocation.
Swaraj's demands are significant considering the fact that the party has been unrelenting on the demand for Prime Minister Manmohan Singh's resignation over which it has disrupted Parliament for two weeks.
"I told her that the Government should announce the cancellation of Coal blocks and institute a fair and independent inquiry," Swaraj tweeted tonight about her telephonic conversation with Gandhi who had called her up yesterday.
Her tweets make no mention of the party's demand for the Prime Minister's resignation.
Swaraj's tweet came after her followers in the micro-blogging site wanted to know the details of her conversation which she herself disclosed.
She said that Gandhi wanted the fortnight-long Parliamentary impasse to end "by our(BJP) agreeing to a discussion."
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Swaraj, however, did not disclose what was Gandhi's response nor did she reply to one of her followers whether her party has dropped the demand for the Prime Minister's resignation.
Gandhi, meanwhile, left for abroad for a week for a routine medical checkup in connection with the surgery for an undisclosed ailment last year.