"The finance minister has assured (us) that whatever best is possible will be done," said a member of the jewellers delegation who met Mukherjee at his North Block office.
Jewellers across the country have been striking since Mukherjee in the union budget March 16 proposed one percent excise duty on unbranded jewellery and doubled the import duty to 4 percent on gold.
Official sources said the government was likely to roll back the one percent excise duty imposed on unbranded jewellery.
However, there was no official announcement in this regard as the decision on roll back has to be taken by parliament.
The agitating jewellers also met Sonia Gandhi and requested her to ask the government to roll back the duties.
Madhukar Chachad, president of the All India Swarankar Sangh, later said that Gandhi had "assured us that she will forward our demands to the finance minister for further action".