The commission examined statements made by the education charity after Andrew Purkis, a former board member of the regulator, asked it to consider whether a publication about what should be in the Conservative Party manifesto, put out jointly by the IEA with the non-charitable Taxpayers’ Alliance, was in breach of guidance on political activity by charities during a general election campaign.
He also asked the commission to reconsider the charitable status of the organisation.
In a letter to Purkis, the regulator said the IEA had removed from its website two press releases that breached commission guidance, including the statement about the Tory manifesto.
The commission’s letter said it also identified a press release called "Labour’s manifesto pledges would add at least £40bn to public spending", which the regulator also considered was in breach of its guidance on campaigning and political activities and charities and elections.
The commission said in its letter that the IEA had reviewed its press releases and other material that had been put on its website since 18 April, when the general election was called, and would "take action to ensure that this material is compliant with our guidance".
It said the IEA had assured the regulator it had put in place a "robust procedure" to ensure that all future releases were appropriately worded for an educational charity.
The regulator said it was content the IEA had acted on its advice and would close its case.
It said it would write separately to Purkis to let him know the outcome of the case "in relation to other issues" raised once it was concluded.
A spokeswoman for the IEA said in a statement: "The IEA is particularly keen in this election period to underscore our strict non-partisan credentials, while also providing a rigorous analysis and commentary on the various policies advocated by all of the political parties in order to improve the public understanding of the role of free markets.
"We have taken independent legal advice on the matter and have chosen to remove from our website two items.
"This is not because of any misgivings about wrongdoing on the IEA’s part, but to ensure that our reputation as an independent educational charity is upheld."
The IEA published the controversial "sock puppets" report in 2012, which said state funding for voluntary organisations that lobby government "subverted democracy and debased the concept of charity".
Work carried out by the IEA in this area was quoted by the government when it announced its anti-lobbying clause, designed to prevent charities from using funds from public bodies to lobby government, although the proposals were subsequently watered down.