Fans of the six clubs involved held widespread protests against the Super League
The Premier League is to bring in a new owners' charter to stop future attempts to join a breakaway Super League.
It follows Manchester United, Chelsea, Liverpool, Arsenal, Manchester City and Tottenham agreeing to join the failed European Super League last month.
All owners will have to sign up to the new rule "committing them to the core principles" of the league with breaches punished by "significant" sanctions.
The Football Association said an inquiry into the six clubs has started.
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"The actions of a few clubs cannot be allowed to create such division and disruption," the Premier League said.
"We are determined to establish the truth of what happened and hold those clubs accountable for their decisions and actions."
The Football Association added: "We wrote to all of the clubs to formally request all relevant information and evidence regarding their participation.
"Once we have the required information, we will consider what appropriate steps to take."
The Super League proposal, which also included some of Europe's biggest clubs, collapsed within 72 hours after widespread criticism from fans, players and governing bodies and politicians.
There have been various calls for sanctions against the clubs, including points deductions, relegation and bans from European competitions.
The executives at the six clubs involved in the collapsed breakaway have been forced to resign from advisory roles at the Premier League.
Most of the clubs apologised and Manchester United's executive vice-chairman Ed Woodward resigned.
In its statement the Premier League said it would also introduce "additional rules and regulation to ensure the principles of the Premier League and open competition are protected".
Both the FA and the English top-flight said it is seeking help from the government to bring in legislation to protect the football pyramid and "the integrity of the football community".
"The events of the last two weeks have challenged the foundations and resolve of English football," the Premier League said.
"These measures are designed to stop the threat of breakaway leagues in the future."
The Premier League also said it "recognises the strength of feeling" among fans but urged protests to remain peaceful.
It follows the protest by Manchester United fans on Sunday which resulted in two police officers being injured and caused the club's match against Liverpool to be postponed.