A Change.org petition calling for those protesting outside Parliament to vacate has now received more than 64,000 signatures.

The petition is called 'Tell the Wellington Protestors to Go Home – They are NOT the majority'.

The petition describes the protesters as 'a disparate group of conspiracy theorists, religious cult members, anti vaxxers, anti mandate believers and flat earthers” and currently aims to reach 75,0000 signatures.

The anti-vaccine mandate protest at Parliament has started its 13th day in soggy conditions after a night of heavy rain in Wellington.

Traffic management remained in place on Saturday to facilitate movement around the periphery of the protest on Parliament grounds.

Police have noted an increase in the number of people attending the protest on Saturday, as was anticipated over the weekend.

The crowd size varied significantly over the course of the day, and an estimated 800 vehicles remain unlawfully parked.

Police continue to have a large presence in the central city, including a team ready to respond to incidents outside the Parliamentary precinct.

Illegally parked vehicles were cleared by Police on Thorndon Quay on Saturday — 15 were moved by protesters after Police spoke with them and two were towed.

Police are also noting the registration of vehicles currently impeding traffic for follow up enforcement action, and structures such as tents and marquees are being removed from any site that does not form part of the main protest area.

The parking facility at Sky Stadium is at capacity.

Police were aware of a planned concert on Parliament grounds on Saturday evening and had serious concerns around the health and safety of such an event.

The inclement weather on Saturday night has done nothing to deter the 1000-plus protesters who now occupy the Parliamentary precinct.

Day 13 of the anti-mandate protest at Parliament grounds in Wellington. Photo: Tom Hunt/Stuff.

A long queue of protesters had formed at a food stall by 7.30am on Sunday for a breakfast of sausages and spaghetti.

Hay on the ground has stopped most of the bog-like conditions that affected the protest last weekend and protesters have been laying mats down on the thoroughfares through the makeshift camp to stop them turning into a mud slick.

"We continue to maintain a highly visible, reassurance presence on site, and staff are engaging with the public and protesters to provide advice and, where necessary, take enforcement action," says a Police spokesperson.

Police have attended at least six medical events within the protest and continue to urge anyone parked unlawfully to remove their vehicle and enable ready access to emergency services.

Police had a presence at smaller protests in Christchurch and Picton on Saturday.

Police say that engagement with the protesters and local authorities is ongoing and there have been no arrests or incidents of note.