Samoa Rugby Union chief executive Faleomavaega Vincent Fepuleai told Radio New Zealand on Monday that Betham had stepped down and that a full review of Samoa's World Cup campaign will be undertaken.
Fepuleai said "Stephen has called it a day...and I think we will go through the proper process in recruitment of a new head coach. The position will be advertised internally and externally and we will secure the best person who we think will take us over the next four years to World Cup success."
Samoa failed to reach the knockout stages of the World Cup after losing to South Africa, Japan and Scotland in pool play.
Samoa Prime Minister Tuilaepa Sa'ilele Malielegaoi, who is also chairman of the Samoa Rugby Union and often a stern critic of the national team, has applauded the players' performance and criticised World Cup referees who, he said, "didn't help our cause."
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
At his regular weekly news conference in the Samoa capital, Apia, Tuilaepa said Samoans should acknowledge their team's performance.
"We must remember that for these sons of Samoa, this is their bread and butter," he said. "If they got injured, that would've been the end of it for them and yet they ignored all that to come and carry Samoa's flag.
"I thank all the players. I acknowledge their hard work in the games that qualified us for the World Cup. I guess it's just that our opponents were very strong."
Tuilaepa attached some blame for Samoa's early exit to referees and match officials.
"Referees need to be consistent," he said. "I have to say that the referees did not help our cause."
Tuilaepa said Samoa also struggled because of a lack of depth and because most of its players are based overseas.
"One of the weaknesses we have is our reliance on our sons overseas, unlike New Zealand where all the players play in New Zealand where they know each other's style of play," he said.
"For New Zealand, they probably have 200,000 players to choose from compared to us where we don't even have five thousand players to choose from. England, Wales, South Africa and others have millions to choose from."
