The president's office said on Saturday that they received a letter of resignation from Sinha, who is now abroad.
Sinha was appointed to the top court as the chief justice in January 2015, with his term scheduled to end on Jan 31, 2018.
"The government has filed 11 cases against him, which is a clear indication that he was forced to resign," said Moudud Ahmed, who sits on the BNP's policymaking National Standing Committee.
The BNP, which formed government three times after 1990 and now is out of parliament after boycotting the last election, had claimed that Sinha was forced to take leave after he went abroad on leave last month.
The ruling Awami League, however, describes it as 'absurd'.
"He has sent his resignation letter from abroad. How can we force him? We did not send a peacekeeping force, did we? These statements are absurd," Law Minister Anisul Huq told the media on Saturday.
BNP leader Moudud came down hard on the government for verbal attacks on the chief justice in the immediate aftermath of the verdict.
The government instead of going for the legal option to seek a review of the verdict turned up heat on the top judge, according to Moudud.
Speaking at a separate event, BNP Standing Committee Member Khandker Mahbub Hossain echoed him.
"He was forced to take leave for health reasons. And now the government forced him to resign," said Hossain, a former vice-chairman of the Bangladesh Bar Council.
Describing the move as a 'blatant attack on the judiciary', he said that it was aimed to 'influence' the judiciary.