Two people, a man in his 20s and a woman in her 50s, were being treated for injuries in hospital on Monday after separate assaults in Dundalk and Longford.
Gardaí have appealed for witnesses to both incidents.
The woman in her 50s was recovering in hospital on Monday after being assaulted at a park in Longford overnight.
Gardaí said the incident took place at the midland town’s Albert Reynolds Peace Park during the early hours of Monday morning.
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A sizeable section of walkway at the rear of the park’s leisure complex, which is also known locally as the Mall, was cordoned off on Monday morning as part of the investigation.
“Gardaí are investigating an assault which occurred in Longford town in the early hours of this morning, Monday, 7th August, 2023,” a spokesperson said.
“A woman (50s) was taken to Midlands Regional Hospital Mullingar to be treated for what is believed to be non life-threatening injuries.”
Longford county councillor Uruemu Adejinmi said the incident had shocked the local community and urged anyone with information to come forward.
“It’s terrifying to think an incident like this can take place in a place like the Mall,” she said.
“My sincerest apologies go out to this lady who should have been safe in what is such a popular public place.”
Cllr Adejinmi added she would also be examining whether additional lighting may need to be erected in the grounds of the local amenity.
In Dundalk, a man in his 20s received serious injuries in an assault on Sunday evening in the Rampart Lane area of the town, gardaí said. He was subsequently treated at Our Lady of Lourdes Hospital in Drogheda.
The assault is said to have occurred around 6.30pm and the scene was preserved for a technical examination after the victim was taken to hospital.
Anyone with information on either incident is asked to contact the Garda confidential line on 1800 666 111 or any Garda station.