The move comes after the council agreed to withdraw unilateral changes to gravediggers' contracts from the 13th August.
Gravediggers in Barry had voted unanimously for strike action after the council demanded they work until 7pm during the summer. An overwhelming result means the workers were consulting on strike dates during August.
Plans to extend the opening hours are still under discussion, with both parties hoping to find a mutually acceptable resolution in the coming weeks.
Cllr Bronwen Brooks, Leader of Barry Town Council, said:
"Following discussions yesterday under the auspices of ACAS, Barry Town Council have agreed to withdraw plans to unilaterally change the contracts of those GMB Members employed at Merthyr Dyfan Cemetery, Barry.
"In return for the GMB having agreed to suspend all industrial action pending meaningful talks to find a mutually acceptable resolution to the dispute."
Mike Payne, GMB Senior Organiser, said:
"We are extremely pleased that both parties have agreed to return to negotiations and to find an amicable outcome to the dispute".