People Before Profit has called on local authorities in Galway to remove monuments, which the party claims glorify slavery and racism.
It wants a monument to Christopher Columbus in Galway to be taken down.
It is also seeking the removal of a plaque in Tuam, honouring Major Richard (Dick) Dowling, who served with the Confederate army in the US.
The Columbus monument, close to the Spanish Arch, was erected to mark the quincentenary of his 1492 voyage to America.
The explorer is reported to have visited Galway around 1477 and the sculpture references his trip to the west of Ireland.
People Before Profit said an absence of any reference to Columbus "genocidal brutality" on the monument is disrespectful.
The party said it instead wants a memorial to acknowledge "Galway's role in the slave trade" as a result of local provisions being supplied to slave traders.
It is also seeking the removal of a plaque from Tuam Town Hall, which references the "outstanding businessman and civic leader" Dowling, who was born near the town in 1837.
The plaque was erected in the late 1990s.
The party said that a 2017 proposal to remove the monument should now be revisited.