IALPA said it needed an urgent meeting with management to clarify a number of issues before it would call off the action.
Ryanair and the pilots union IALPA are locked in a stand off, just days ahead of Wednesday's planned strike.
Chief executive Michael O'Leary said the airline would reconsider its policy of refusing to recognise labour groups.
Ryanair said on Friday that recognizing unions would be a "significant change", but that it hoped to have new structures agreed early next year.
And Ryanair released a statement today and said they can meet with Impact on Tuesday "if that would suits them better".
During a conference call with the pilots, Mr O'Leary is understood to have said that the offer of union recognition from Ryanair today is genuine.
In the face of threatened industrial action by pilots at some of Ryanair's main bases, the airline announced last week that for the first time it would recognise and negotiate with pilots' unions across Europe.
The strike is planned for Wednesday 20 December.
Mr O'Leary spoke to the airline's chief captains across its nearly 90 bases. A spokesman for Ryanair said on Saturday morning there was no update on this position.
However, the airline had said that management would not be able to meet with IMPACT representatives until Wednesday.
"Once we have that we're ready to lift the industrial action but we need to do that first".
"Given the seriousness of the situation I think it would be good if they could move their diaries around and find availability", he said.
Ryanair has sought a meeting with the Irish Airline Pilots' Association on that day, according to The Independent.
Liz Blackshaw, International Transport Workers' Federation campaigns director, confirmed on Friday the organisation had written to Ryanair seeking recognition for unions representing cabin crew.