Two iconic Australian monuments linked to its colonial past have been damaged and defaced in what authorities described was a serious act of “vandalism” near Melbourne’s central business district on a national day of mourning for victims of the Bondi Beach terror attack.

The Pioneer Monument in Melbourne’s Flagstaff Gardens, erected in 1871, was found toppled and broken into pieces early on Thursday, with graffiti sprayed across its base. The damage is believed to have occurred overnight.

Nearby, the Separation Memorial, which commemorates Victoria’s political separation from New South Wales, was also targeted but remained standing.

Victoria’s premier Jacinta Allan strongly criticised the incident, describing it as a “disgrace”.

“Even on a day about love and unity, these people can’t help but introduce hate and destruction,” she said.

“The groups who continue to commit these crimes must face the full force of the law.”

Incidents targeting statues tied to colonial history have increased in the lead-up to Australia Day on 26 January in recent years.

The holiday is celebrated by many Australians with barbecues and day trips to the beach, and is also a popular date for immigrants to receive their Australian citizenship.

But for many activists, Australia Day is known as “invasion day” as it marked the beginning of a sustained period of discrimination and dispossession of Indigenous peoples without the negotiation of a treaty.

According to the City of Melbourne website, the Pioneer Monument was designed by Samuel Craven and honours early European settlers buried nearby.

Its inscription reads: “Erected in 1871 to the memory of some of the earliest of the pioneers of this colony whose remains were interred near this spot.”

The Separation Memorial, installed in 1950, marks the centenary of the proclamation of Victoria’s colonial government.

Red triangles were also painted on both monuments – a symbol experts say has violent connotations.

“We’ve seen it pop up at some of the protests on signs, on T-shirts and basically on stickers and so on,” Deakin University extremism expert Josh Roose was quoted as saying by the Australian Broadcasting Corporation.

“It’s used by Hamas to designate, in their propaganda, a target.

“It’s a symbol that’s inherently violent.”

Police confirmed an investigation is underway and believe heavy equipment was used to pull down the Pioneer Monument. The damage is estimated to have occurred between 10pm on Wednesday and 6am on Thursday.

Melbourne lord mayor Nick Reece said: “Defacing or damaging city assets in Melbourne will not – and cannot – be tolerated. We can have a debate about the future of statues and memorials, but we will never tolerate or reward vandalism.”

Last year, in the run-up to Australia Day, a century-old statue of Captain James Cook was sawn off at the ankles, and another of Queen Victoria was doused in red paint.