Sinn Fein is seeking a meeting with the PSNI following the theft of election posters.
A video of masked men taking down posters in Portadown is circulating on social media.
Sinn Fein says most of its posters have been taken down in Banbridge while some posters were removed in Lurgan.
Paint was thrown at a poster of John O’Dowd in Banbridge at the weekend.
Cllr Liam Mackle, who sits on Armagh, Banbridge and Craigavon Council and is standing in the forthcoming NI Assembly elections in Upper Bann, said: “Banbridge town has been practically stripped of SF posters. In Portadown masked loyalists ripped posters from poles and Lurgan has also seen significant losses.
“The scale of theft and destruction of SF posters in Upper Bann is on a scale which means the police must respond to protect democracy.”
Meanwhile his party colleague John O’Dowd, who is also standing for election in Upper Bann reported online threats to vandalise a Sinn Féin election billboard in Banbridge to the police. This was subsequently destroyed when paint was thrown at it.
Mr O’Dowd said: “Contributors to the social media debate discussed how best to remove or deface the billboard.
“One contributor suggested a pot of paint, with another encouraging it to be attacked under the cover of darkness.”
Chief Inspector Lynne Corbett said: “Police in Armagh, Banbridge and Craigavon are committed to doing everything we can to ensure all candidates can participate fully in the forthcoming Northern Ireland Assembly election free from harassment, intimidation and other forms of criminality.
“We are investigating thoroughly all incidents which have been reported to us, including the removal and destruction of election posters, and any identified suspects will be liable to prosecution.
“I would be happy to engage with any person or party with concerns on this matter and would appeal to anyone who witnesses the theft or damage of election posters to contact police immediately.”