Socialist Party leader Joe Higgins has signalled that Clare Daly's public support for Independent TD Mick Wallace could make it difficult for some members of his party to work with her as part of the United Left Alliance.
Mr Higgins said he deeply regretted the departure of Ms Daly from his party.
He said very serious disagreements had emerged in June and July because of the public and political support she gave to Mr Wallace in the wake of revelations of his tax evasion.
Ms Daly resigned from the Socialist Party at the weekend and said she will "redesignate" herself as a United Left Alliance TD.
She had been criticised by some in the party for her support for Mr Wallace after it emerged that his company had made a false VAT declaration to the Revenue Commissioners.
Ms Daly said she believed it was time to prioritise the building of the ULA.
"Unfortunately the potential of the ULA has not been fully realised and it is now time that the component organisations prioritised the building of the ULA."
Ms Daly described suggestions that her decision to resign from the party was because of her connection to Mr Wallace as "absolute nonsense".