The weather service in Samoa says tropical Evan has moved away from the capital, Apia, and strong winds are now buffeting the smaller islands off the northern coast of Savai'i.
It says the rain has eased and damage assessment teams should be able to begin work today.
The police in Samoa say two people have been killed.
Two children are missing presumed drowned, and at least five other people are also missing.
The assistant chief executive of the Meteorological Division Mulipola Ausetalia Titimaea says the cyclone is now about 100 kilometres away from Apia.
"The current position is north-north west of Apia, it's must closer to Savaii at this time. The tropical cyclone is moving west north west at a speed of 6 miles per hour at this time we are still monitoring the situation but there is very little chance of looping back to the islands."
Samoa's Disaster Management Office says about two thousand people evacuated from flooding have sought refuge in emergency shelters around Apia.
A spokesperson, Filomena Nelson, says more than ten emergency shelters have been established.
The government is providing that and also relief supplies like food and non-food items mainly blankets and clothing. We have more than 2000 people in the shelters that we have established but other people have evacuated to their other relatives who live on higher ground.
She says today, damage assessment teams will begin inspecting the devastation on the island of Upolu.
She says search and rescue teams have reported damage to houses, roads and the water and electricity infrastructure.
Filomena Nelson says there's likely to be extensive damage to the island's agriculture.
Most likely we will go out and do damage assessment throughout the island of Upolu first because at this stage the cyclone has moved over the island of Savaii so we will not be able to go over there until the cyclone is well away from us.
The storm is expected to hit Fiji next, and the authorities are preparing for the worst.
The Fiji metservice says tropical cyclone Evan is intensifying as it moves towards Fiji.
It says the cyclone has now been upgraded to a category four system with winds close to the centre of up to 165 kilometres an hour with momentary gusts of 230 kilometres an hour.
A tropical cyclone alert and a strong wind warning is now in force for Fiji's Vanua Levu, Taveuni and nearby smaller islands and the Northern Lau group.
A damaging heavy swell warning is also in force for Vanua Levu, Taveuni and nearby smaller islands and Northern Lau group.
The lead forecaster at the Fiji metservice, Misaeli Funaki, says warnings have also been issued for the Niua group of islands in Tonga.
He says Fiji should start feeling tropical cyclone Evan by Sunday.
The eye of Evan will move towards the north of us and the winds are still going to be experienced by Fiji. We are looking at the later part of Sunday we should be feeling it in Fiji, mainly to the islands which we are warning for and as it comes in we will probably have to include the other islands.
Misaeli Funaki says they expect tropical cyclone Evan to leave Fiji waters on Tuesday.
The Ministry of Information says Evan is likely to be the most powerful cyclone to hit Fiji since 1993.
Fiji's interim prime minister, Commodore Frank Bainimarama, addressed the nation saying Evan will affect the whole country.
It has winds of up to 180 kilometres power which may intensify, and if the weather forecasters are correct, it will affect Fiji in a very damaging way bringing about destructive winds and flooding, fellow Fijians I can not stress enough how serious this is, every Fijian will be affected.
Fiji's interim leader, Frank Bainimarama.