"But with all tropical cyclones, there remains some uncertainty associated with the forecast track," meteorologist Georgina Griffiths said.
There was a "fairly solid" chance the cyclone would come near northern New Zealand by this weekend.
"At category 3, it's still a significant system and on a southerly track it could come closer to the North Cape or somewhere in the middle of the Tasman Sea if it heads more towards Australia," she added.
"Either way, Northland will be the first to feel its effects. The easterly winds will pick up but there won't be gales. Easterly swells will increase with possible storm surge and onshore winds."
Ms Griffiths said the already-stifling humidity experienced throughout the country but particularly in Northland would get worse as the week progressed.
She said with the tropics so abnormally warm from the effects of El Nino, tropical cyclones were inevitable.
"Winston did a really big loop in very warm Pacific waters and because of the prevailing warm weather, it can get its energy from anywhere but we're not likely to see its effects before Friday."
Weather watches or warnings can be accessed at metservice.com, on m.metservice.com, MetService TV, at MetService New Zealand Facebook, @metservice and @MetServiceWARN on Twitter and at blog.metservice.com.
Meanwhile, a Whangarei truck driver who was stranded in Suva was expected to fly out of Nausori Airport yesterday. According to a family member, Rabendra Prasad was rescheduled to board a Fiji Airways flight at 9am yesterday.