Intercity and commuter rail services and Dublin Bus and DART services were seriously affected on Friday morning.
Rail and bus services crossing the Irish border were also impacted as a result of the action.
But, Enterprise trains and Translink coaches between Dublin to Belfast have resumed and are running as normal.
Bus Éireann services from Belfast to Dublin Airport and Dublin city, and from Londonderry to Dublin are not operating as a result of the strikes.
Translink is advising people hoping to use its services to check its website and social media for updates.
Staff at Bus Éireann have been on strike since last Friday in a dispute over cuts to pay and working conditions.
Management has said the changes are essential to avert the prospect of insolvency at the loss-making company.
The company said the vast majority of services were not operating as a result of the action.
The National Bus and Railworkers' Union (NBRU) said it had told its members that the unofficial pickets should be removed as they had not been sanctioned by the union.
He added that all workers at Iarnród Éireann and Dublin Bus who are members of the NBRU should be at work as normal.
He apologised for the inconvenience to travellers and said he was angered when he heard of the action, which his union would not support.
Mr O'Leary said, however, that Bus Éireann drivers were frustrated and they way they are being treated by the company is an "absolute disgrace".
Irish Transport Minister Shane Ross said he was "actively monitoring developments" and said he regretted the impact on passengers.
Some bus and rail services in the Republic of Ireland have returned to normal after unofficial pickets linked to a Bus Éireann strike were lifted.