Unite attacked the "scandalous behaviour" of the Scottish site's owners Ineos, but said it wanted to protect the national asset.
Union members were due to walk out for 48 hours from Sunday over the treatment of Unite convenor Stephen Deans.
Lengthy talks were held at the conciliation service Acas but they ended at 5am today without agreement.
Unite accused the company of "walking away" after 16 hours of talks.
Unite's Scottish Secretary Pat Rafferty said: "We are outraged that Ineos representatives walked away from Acas talks, after 16 hours of negotiation and on the cusp of an agreement, for the ludicrous reason that Ineos chairman Jim Ratcliffe instructed his management representatives to demand an apology on his behalf.
"Unite offered Ineos every proposal we could practically make, specifically an offer to enter into negotiations under the auspices of Acas to secure the future of Grangemouth with the immediate call-off of all industrial action and a guarantee of no strikes during these negotiations.
"However at 5am this morning Acas representatives informed us that we could not conclude an agreement to take to our members because a list of fresh demands were placed upon us and because 'Jim wants an apology' and that this was 'a deal-breaker'.
"I have never came across anything like this in over 30 years of employment relations and it is utterly reprehensible."
Unite accused Ineos of running the Grangemouth refinery and petrochemical sites into a "damaging cold shutdown" which will impact on fuel production and supply across Scotland.
"The safety and integrity of the site and the local population are now paramount and we have an obligation to ensure that Ineos does not permanently decimate the plant's assets and the workforce with this cold shutdown," Mr Rafferty said.
"As a result, Unite will now call off all industrial action with immediate effect in order to protect this national asset from the scandalous behaviour of its owner.
"The plant should now start the return to full production and there is no excuse for this not happen."
Mr Deans was involved in the row over the selection of a Labour candidate in Falkirk, where he is chairman of the constituency party.
He was suspended by Ineos and later reinstated, but is facing an internal investigation by the company over issues linked to the Falkirk affair.
Ineos has warned that Grangemouth is losing £10million a month and will close in 2017 without investment and cost-cutting.