The FAST Party deputy Tuala Tevaga Iosefo Ponifasio told RNZ that there's no doubt his party is now the government.
He said they were forced into holding Monday's swearing-in ceremony outside parliament.
"According to the constitution, the head of state is supposed to swear in, and if not the head of state then it will be a council of deputies. But none of those were available. They didn't want to be part of this," he said.
"So as far as we're concerned, we formed the government within the 45 legal days and we've done the swearing in and we do have a government."
An eminent political scientist in New Zealand agrees.
Political analyst at Pacific Linc, Dr Christina Laalaai-Tausa, said the processed followed was legal, and as of today, the Prime Minister-elect is FAST leader Fiame Naomi Mata’afa.
"All the power that that Tuilaepa and his party had, should now be relinquished, and people should be following and listening to Fiame from now on, and that is what the court order said, and that is what the majority of the voters voted for.
"The two most important things in a democracy is privilege and the people's voices and upholding the rule of law, as per the constitution."
But HRPP leader Tuilaepa Sailele Malielegaoi has repeated his claim that FAST had committed a coup.
"This is what happened, they have broken the law, they have disgraced the chief justice, they have disgraced our country.
"The head of state proclaimed that there would be no parliament sitting, so too did the speaker - which begs the question, what was the chief justice even thinking? It makes you wonder, where is our judiciary headed?
"FAST held a swearing-in ceremony where the chief justice was absent, so what exactly happened yesterday? They've taken away the duties of the chief justice and the head of state and acted in what seems to be their own power, and that to me, is a definition of a coup."
But deputy FAST leader Tuala said they weren't concerned about Tuilaepa and the HRPP's claims to still have power.
He said FAST were meeting to discuss their next moves and it was obvious they would have to head back to court.
The crisis is now drawing in leaders from other countries.
The former Marshall Islands president Hilda Heine, who was the first woman head of state in the Pacific, has offered congratulations and support to Fiame Naomi Mata’afa.
Heine tweeted: "Stay strong and unwavering in your legitimacy as the duly elected Samoa PM! The facts of the election stand. Your win is a win for Pacific women. The political wrangling, fueled by entrenched resistance to change is sad but not surprising."
Photo file FAST Party