More on KentOnline
A medical situation involving a pregnant woman means the travellers who pitched up on Friday won't be leaving before the end of the day.
The group of Irish travellers moved onto Woodlands Park off Wrotham Road, on Friday, parking caravans and cars and setting up tents.
It follows similar recent instances of travellers setting up in Borstal Recreation Ground in Rochester and in Central Park, Dartford on Friday night, before moving on.
Police said they were notified at 7.40pm on Friday, and say it is the responsibility of the land owner to arrange eviction.
A council spokesman said: "On Sunday a council official accompanied by a police officer gave the travellers notice that they must leave the site, which is owned by Gravesham Borough Council.
"The travellers said there was a medical situation involving a pregnant woman and that they intend to leave on Monday evening.
"Police have been monitoring the site and liaising with council officers. No incidents have been reported. The council is preparing to obtain a court order for the trespassers to leave should that become necessary.
VIDEO: The group will remain on the park for the rest of the day.
"Council officers will be going to the park today to assess the situation in the light of there being a number of children in the camp.
"There is a required procedure to deal with such unlawful camps and the council is obliged to follow the appropriate steps. The council would like to assure residents that all possible steps are being taken."
A popular park in a residential area, Woodlands Park was recently subject to a £150,000 refurbishment scheme - with workers intalling new play equipment including a roundabout, steel cableway, basket seat swing, rope swing and a slide unit.
Cllr Mick Wenban (Con), who represents Woodlands ward, said he and fellow ward councillor, Sara Langdale, had been down to the park on Friday to check out the situation.
He said: "It's disappointing, given they are right in the middle of the park, that the children have been unable to play football there over the weekend."