The service says as of 5am local time, severe tropical cyclone Jasper was about 400 kilometres southwest of Rennell Island.
Wind alerts are still in place for Rennell/Bellona Province and most waters.
Rain showers with thunderstorms are still expected for all provinces.
It said Jasper is moving into the Coral Sea and away from the Solomon Islands region and towards northern Queensland.
As a category 4 storm, and now as a Severe Tropical Cyclone, Jasper can be expected to have winds, at its centre, of up to 204 kilometres an hour.
Weatherwatch reports that as the storm moves across open water it is picking up intensity, and this is expected to peak by late on Friday or early Saturday as it moves southwest.
Progress is slow because of a large high in the Tasman Sea.
Weatherwatch predicts the cyclone is likely to weaken as it approaches Queensland but that it is still likely to have a substantial impact, affecting a wide area from Ingham, near Townsville, through to Cooktown in the north.
Impacts
The Solomon Islands Water Authority has extended the suspension of water from the Kongulai and Kombito sources.
Authority chief executive Carmine Piantedosi said the clarity levels at the two water sources are at unsafe levels.
She said it was a precautionary measure to turn off the supply to avoid providing unsafe water for consumption or use.
A boil water advisory is in effect for Honiara until further notice.
Meanwhile, the current bad weather situation has forced shipping operators to cancel their trips to most of the provinces.
With the festive season nearing its peak, people are now planning to travel back to their provinces.
However, the negative impacts of Cyclone Jasper are felt nationwide, and most ships are taking shelter at nearby harbours and bays in the Central Province.
A notice issued by Franjit Shipping Service on Thursday local time, advised the public and passengers of the cancellation of its services to Auki this week.
This was due to the adverse weather conditions.
Fairwest Shipping Company operating along the Honiara - Western route also issued an advisory about the cancellation of Fair Lady's trips.
It stated that MV Fairlady on Monday had taken shelter from the cyclone at Ringi Cove in the Western Province.
Another Fairwest Shipping vesse,l MV Marina II, which operates a weekly service along the Honiara-Western route, was forced to delay its return trip from Gizo to Honiara this week.
It was supposed to depart Gizo on Monday morning for Honiara.
However, it advised that once the weather improves, it would leave Gizo for Honiara on Friday morning local time.
Local media is also reporting that Solomon Airlines has also suspended its domestic flights since Tuesday this week due to the current bad weather.