Taoiseach (Irish PM) Micheál Martin said the Republic of Ireland could not “risk moving backward”.
The next phase would also have allowed gatherings of up to 500 people outdoors and 50 indoors.
Mr Martin said the decision would be reviewed again in three weeks time.
It is the second deferral of Phase 4 after the Irish cabinet voted to delay it in July amid concerns about the spread of the virus.
The current rules on gatherings allow for a maximum of 200 people to meet outdoors and 50 indoors.
On Tuesday, the cabinet also made changes to the green list for travel and announced face coverings will be mandatory in shops and shopping centres from Monday 10 August.