NSW Premier Gladys Berejiklian says her government will consider laws to better protect monuments after a second statue of Captain Cook was vandalised in Sydney at the weekend.

The century-old statue, at the junction of Belmore Road and Avoca Street in Randwick, was sprayed with paint on Saturday night.

A council spokesperson said the graffiti had already been cleaned up, after rangers spotted it on Sunday.

“We are currently working with local police who are investigating the vandalism,” they said.

It comes after a part-time worker in NSW Greens MP David Shoebridge’s office was charged after a statue of Captain Cook in Sydney’s Hyde Park was defaced at the weekend, in a separate incident.

Police guarded a statue of James Cook in Sydney’s Hyde Park on Friday. Photo: AAP

Ms Berejiklian said she would consider tightening laws to prevent attacks.

“I wish it didn’t come to this and I want to stress that it’s only a very, very small percentage of the population that’s engaging in this activity, the vast majority of us don’t condone it, we think it’s disrespectful, it’s un-Australian,” she said.

The statues of early colonialists Captain Cook and Lachlan Macquarie in Hyde Park have been previously targeted by vandals, particularly around Australia Day.

But the issue is not unique to Sydney.

In Melbourne, Captain Cook’s Cottage also had a police guard at the weekend.

The swathe of global Black Lives Matter protests have put a spotlight on many monuments critics argue fail to recognise historical violence and inequalities.

A statue of former British prime minister Winston Churchill in London was covered in protective cladding at the weekend to stop it being vandalised, while in the US, several statues of Confederate general Robert E Lee have been removed.

The boxed-up statue of Sir Winston Churchill in Parliament Square, London at the weekend. Photo: AAP

Meanwhile, two women, aged 27 and 28, were arrested on a street near Hyde Park and were allegedly found with a bag containing spray cans after the statue was vandalised on Saturday night.

Charmaine Morrison-Mills, 27, and Greens staffer Xiaoran Shi, 28, appeared in Parramatta Bail Court on Sunday on charges of destroying or damaging property and possessing a graffiti implement.

They were both granted bail to appear in Sydney’s Downing Centre Local Court on July 2 and are banned from entering Hyde Park.

There is no suggestion the graffiti on the Randwick statue and Hyde Park statue are linked.

“I understand that one of the two people charged regarding the incident involving the statue in Hyde Park has part-time employment with my office,” Mr Shoebridge said.

“They were not engaged in employment at the time of the incident, which occurred well outside of work hours.”

Two police cars remained stationed at statues of historical figures overnight.

The Premier called on Mr Shoebridge to apologise for the incident and condemn Ms Shi’s alleged behaviour.

On the appropriateness of continuing to memorialise Captain Cook in statue, Ms Berejiklian said: “We need to respect those milestones which have made a difference in our history.”

“I’m proud of the fact we have the oldest continuing culture on the planet in our indigenous population, proud of the fact we have a colonial history, a migrant history, a history which respects our veterans.”

-with agencies