Security forces recovered part of a rocket propelled grenade launcher during a search near Seaforde in Co Down on Saturday, according to local representatives.
It's not yet know whether the find was functional, or something which has lain at the wooded site for years.
The PSNI has not confirmed the find, but local politicians told the Belfast Telegraph they had been assured by security force sources that an RPG part was involved.
Ulster Unionist councillor Alan Lewis said: " This is undoubtedly a worrying development.
"Firstly I would like to commend the police and army on their swift and diligent response.
"Secondly however, I question what those mindless criminals behind this behaviour have to offer society.
"This incident just adds to a series of dissident republican activities in the south Down area.
"This puts a horse and cart through the theory dangled by those advocating the avoidance of an Irish hard border that it would deter future republican terrorism.
"The people of south Down don't want or support these actions and I appeal to anyone in the local area with information to please contact the police."
The discovery was made on Saturday in woodland at the Old Park Road, around half a mile from the village of Loughinisland.
"The discovery was made by someone doing a 'litter pick' at the side of the road, " SDLP MLA Colin McGrath said.
"But we don't know if it had been lying there for 20 years, or for 20 minutes," he said.
"It's a very worrying find."
In a statement, the PSNI said: "Investigations into the security alert, where a suspicious object was recovered in Seaforde are still ongoing. The object has been taken away for further examination. There are no further details at this stage."
Meanwhile, roads in Co Antrim were closed on Sunday following another security alert near Ballymoney.
Bann Road and Glenstall Road at Bendooragh were closed for several hours as Army bomb disposal experts examined three suspicious objects discovered in the area on Sunday.
Two of the objects were found to be fireworks and the third object was nothing untoward, police said.
All roads have now re-opened.
The weekend security alerts came after it was learned that Army bomb disposal units in Northern Ireland had been called out 264 times in 2020.
The information emerged after a parliamentary question from East Londonderry MP Gregory Campbell.
Of the 264 call-outs, 103 were related to "suspicious items", of which 70 were found not to be viable devices.
MI5 currently categorises the threat to Northern Ireland from terrorist groups based here as severe. Mr Campbell said the penalties for those found guilty of planting viable or hoax devices should be "significantly increased".
The DUP politician said punishments must take account of "not just the inconvenience, but the potential loss of life".
"Given their activities I think the people behind these attacks are unlikely to stop, but I think the message from wider society and the Executive and Justice Minister needs to be that if they don't stop the penalty will be very severe," Mr Campbell said.