The BMS' decision to pull out was taken at a meeting of its core committee here in the capital.
Yesterday, at a meeting of 11 central trade unions, BMS had suggested calling off the planned strike following the government's assurances and offering a six-month implementation window.
However, the remaining 10 trade unions decided to stick to their guns.
"Since the government has come forward with positive assurances on our basic demands and assured us to continue dialogue, BMS decides to defer the strike for the time being," BMS General Secretary Virjesh Upadhyay told PTI after the core committee meet.
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These unions are expecting around 40 crore organised and unorganised workers to join the proposed strike on Wednesday.
Elaborating, he said, "Strike is not the best way out at present. After the assurances by the government, opting for a strike means it's being done for political motives."
A high-level group of senior ministers had met the top union leaders on Wednesday and Thursday to convince them of withdrawing the strike call and had also promised to look into their various demands, including minimum wages, contract labour and social security.
The ministerial panel had also proposed to raise the ceiling of bonus, widening the coverage of the provident fund and health insurance to include workers from construction as well as schemes such as aanganwadis.
The panel comprising Oil Minister Dharmendra Pradhan, Power Minister Piyush Goyal and Minister of State in the Prime Minister's Office Jitendra Singh had two rounds of meeting with the trade unions in as many days.
BMS asked other central trade unions yesterday that the government should be given at least six months to deliver on these assurances.
The meeting of BMS core committee was presided over by its President B N Rai.