The Laigin had suffered a crushing defeat at the Battle of Áth Senaig (Ballyshannon, Co.Kildare) in 738 at the hands of the high king Áed Allán mac Fergaile (died 743) of the Cenél nEógain. In Muiredach's reign good relations were maintained with the high king Domnall Midi (died 763) of the Clann Cholmáin. In 759 Domnall led a host of the Laigin as far as Mag Muirtheimne in Ulster.
The Uí Máil branch of the Laigin had at times held the kingship of Leinster; the last being Cellach Cualann mac Gerthidi (died 715). In 744 The final attempt by the Uí Máil seems to have been defeated at the Battle of Ailén dá Berrach in Cualu. Two of Cellach's grandsons, Cathal and Ailill, were slain.
Attacks by the Osraige king Amchaid mac Con Cherca also occurred during Muiredach's reign, including an attack on the Fotharta Fea in 754.. However these seem to have involved the southern Laigin, the Uí Bairrche and Uí Cheinnselaig.
Muiredach was ancestor of the Uí Muiredaig sept of the Uí Dunlainge with their ryal seat at Maistiu (Mullaghmast) in south Kildare in the territory known as Iarthair Liphi (western Liffey). His son Bran Ardchenn mac Muiredaig (died 795) was also king of Leinster.