They hacked through an ornamental solid brass chain from the monument dedicated to Inverclyde's war dead in the Wellpark and made off with it.
An off-duty fireman walking his dog made the discovery on Monday morning and alerted the park keeper, who called police.
Inverclyde's Provost Michael McCormick, pictured, has condemned the culprits as 'sick'.
He said: "Quite frankly, I am disgusted that anyone could stoop so low.
"The culprits behind this appalling act of vandalism have insulted the memory of the people from Inverclyde who laid down their lives for their country.
"Our armed forces are very much in our thoughts at the moment as we prepare to honour their members past, present and future on Armed Forces Day on 26 June and I am sure everyone in Inverclyde feels as angry and revolted by what has happened as I do."
An Inverclydce Council spokesman said the figure of winged Victory on the marble monument had been tampered with and a bronze St Andrew's Cross and a bronze lamp are also missing.
Provost McCormick said the memorial was built to recognise the 1,500 young men from the area killed during the First World War and has become a focal point for acts of remembrance since.
He added: "At a time when on an almost daily basis we hear of another family given the sad news of the death of a loved one in Afghanistan and Iraq, we should all be showing our support and gratitude for the men and women who make up our armed forces community.
"I hope someone's conscience will see the safe return of the missing items so we can restore the memorial."
Greenock pensioner George Gray, who was recognised for his role in the Arctic convoys during the Second World War, also hit out at the vandals.
The 83-year-old said: "It's disgraceful. These people have no thought for anybody."
Sandy Burke, owner of A. Burke and Son Scrap Merchants, said: "I estimate it would cost around £2,000 to replace the chain."
Park-keeper Derek Robertson says Wellpark is a popular place for tourists and schoolchildren to visit. He said: "It is a disgrace that this could happen to a war memorial."
Mr Roberston says security will now be stepped up, with gates being installed at the
bottom of the park and no vehicles allowed through the top gates.
John Thompson, 52, who was enjoying the sunshine in the park yesterday, said: "It's scandalous. The monument should be respected, not abused."
Police have been carrying out door-to-door inquiries. They believe bolt croppers could have been used to cut the chain.
Inverclyde's police area commander Graeme MacDiarmid said: "This theft is totally unacceptable.
"I am sure that the residents of Inverclyde will join with me in condemning such a disrespectful act.
"The armed forces are currently engaged in a war on terror in Afghanistan and war memorials give the public the opportunity to pay their respects to the fallen."
Anyone with information should call Greenock police on 492500.