Gilligan did not want to explain how they are connected, but did say that the investigation has been marked by international cooperation so far, and that it will continue to do so.
"The operation is a result of an investigation that has been going on since the summer of 2009."
The American Justice Department has earlier refused to comment on whether she was connected to the suspects in Ireland, and has yet to confirm the report.
Colleen LaRose, a US citizen who is 47 years of age and also goes by the names Fatima LaRose and "Jihad Jane," has been held in custody in Philadelphia since October 2009.
A federal indictment accuses her of agreeing to kill a Swedish citizen and travelling to Europe for this purpose. It says she also contacted the Swedish embassy last March asking for instructions on how to acquire permanent residency status in Sweden.
Several American media outlets report that she had traveled to Sweden as late as fall 2009 to plan for the attack.
According to a statement from the US Justice Department, LaRose and five others who haven't been charged recruited men on the Internet "to wage violent jihad in South Asia and Europe, and recruited women on the Internet who had passports and the ability to travel to and around Europe in support of violent jihad."
John Gilligan of the Irish Police reports that just one of the seven people arrested yesterday holds an Irish passport. But he does say that every one of them has been living legally in Ireland, and that "one is American and most of the others are from North Africa."
He cannot say if any had traveled to Sweden, as LaRose had.
She wrote in an email in February that her blond hair and blue eyes help her pass unnoticed in Europe.
LaRose is charged with "conspiracy to provide material support to terrorists, conspiracy to kill in a foreign country, making false statements to a government official and attempted identity theft."
Court documents reveal that a man from South Asia wrote an email to LaRose telling her to "travel to Sweden, find Vilks, and kill him."
She reportedly answered him with the message: "I will make it my goal until I succeed, even if it costs me my life."
If found guilty, she faces life in prison.