The headway was achieved after a meeting of the Empowered Committee of State Finance Ministers' Chairman A R Rather with Union Finance Minister Arun Jaitley late in the evening.
After three rounds of discussions during the day -- one of the empowered commitee members and two with Jaitley -- the Centre offered an olive branch to the states who have been holding up the bill because they did not want petroleum products and entry tax to be a part of the GST regime.
States have said they will respond to Centre's proposal shortly, sources added.
"We have made some headway. We will meet the Union Finance Minister again in a week's time," Rather told reporters after a series of meetings through the day.
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Minister of State for Finance Jayant Sinha also said that a "very good progress" has been made.
The fine print of "progress" could not be ascertained.
The Centre wants to introduce the GST regime, hanging in balance for last 6-7 years, by April 1, 2016.