The Mandate trade union has welcomed Tesco's agreement to enter talks "without prejudice" with a view to settling the current dispute over contracts for long-serving workers hired before 1996.
Tesco management wrote to Mandate agreeing to talks in a bid to resolve the row.
It is understood a meeting will be set up in the coming days.
Mandate members at eight Tesco stores began an indefinite strike on Tuesday, and a further eight stores are due to join the strike tomorrow.
23 stores will be balloted for strike action from Monday.
So far all stores have remained open, despite the pickets.
Mandate General Secretary John Douglas said that while the union welcomed the company's response to the union's call for "without prejudice" talks, they remained cautious as the company had said the solution to the dispute is "as set out by the Labour Court in its recommendation".
That recommendation was rejected by the 250 pre-1996 staff at the centre of the row - and the union insists a solution cannot be found totally within the confines of that recommendation as it currently stands.
In a statement earlier, Tesco stressed that the company has always been open to constructive dialogue to reach a reasonable, fair resolution to the changes to pre-1996 terms and conditions.
The company noted that it had attended ten WRC conciliation conferences and a Labour Court hearing, and had always adhered to the industrial relations process - including accepting the Labour Court recommendation in full .
Tesco reiterated that the solution to the dispute is as set out in that Labour Court recommendation, saying Mandate should also endorse it.
The company said it was a matter of serious concern that Mandate officials had told some workers that "they are next" - a claim which management described as false, and causing significant distress and concern.
It said that concern had been compounded by Mandate's call for shoppers to shop elsewhere.
TDs accuse Tesco of 'union-busting attitude'
The ongoing strike has been raised by Opposition TDs during a Topical Issues debate in the Dáil, with Sinn Féin's Aengus Ó Snodaigh saying it is "an absolute disgrace" that Tesco workers had to go on strike to demand their rights.
He accused Tesco of "a union-busting attitude" and infringing on the terms and conditions of its workers.
He called on the State to step in an prevent a company as profitable as Tesco from slashing wages and attacking rights.
A number of other TDs also criticised the action by Tesco, calling on the Government to intervene.
In response, Minister for Jobs Mary Mitchell O'Connor said she had no "direct role in the resolution of this or similar disputes."
The Minister urged both parties to use the WRC and Labour Court, welcoming the announcement that both sides have agreed to more talks.
List of stores already on strike:
Currently, the staff in the following eight Tesco stores are on indefinite strike:
Tesco, Baggot Street Lower, Dublin 2
Tesco, Ballyfermot Rd, Ballyfermot Upper, Dublin 10
Tesco, Clearwater Shopping Centre, 11 Finglas Road, Dublin 11
Tesco, Manor West Retail Park, Rathass, Tralee
Tesco, Rear Main Street, Deanscurragh, Longford
Tesco, Navan Town Centre, Kennedy Rd, Dillonsland, Navan
Tesco, Tullamore Retail Park, Portarlington Road, Cloncollig, Tullamore
Tesco, Vevay Road, Bray
Stores to join strike from Friday 17 February:
Tesco, Artane Castle Shopping Centre, Kilmore Rd, Beaumont, Dublin 5
Tesco, Churchview Road, Kilbogget, Ballybrack
Tesco, Roselawn Shopping Centre, Roselawn Rd, Blanchardstown, Dublin 15
Tesco, 22A Drumcondra Rd Upper, Drumcondra, Dublin 9
Tesco, Phibsborough Shopping Centre, Phibsborough Road, Phibsborough, Dublin 7
Tesco, Park Shopping Centre, Prussia Street, Arran Quay, Dublin 7
Tesco, Unit 9 /10, Monaghan Shopping Centre, Dawson St, Tirkeenan, Monaghan
Tesco, Kilcoole Rd, Rathdown Lower, Greystones