The Swiss Federal Office of Justice (FOJ) has confirmed the two FIFA officials arrested on Thursday morning are Alfredo Hawit, president of CONCACAF, and Juan Angel Napout, president of CONMEBOL.
Both Honduran Hawit and Paraguayan Napout were taken into custody by Swiss police after raids at the Baur au Lac hotel in Zurich following arrest requests made by the United States. Both men are suspected of accepting bribes of millions of dollars.
After hearings with the Zurich cantonal police, the FOJ has announced Hawit and Napout are opposing their extradition to the US.
In a statement, the FOJ added: "The FOJ will now ask the USA to submit formal extradition requests within the 40-day deadline laid down in the bilateral extradition treaty.
"Extradition proceedings will be resumed as soon as these requests have been received. Until the FOJ, as the court of first instance, has issued its ruling, the persons concerned may still agree at any time to simplified extradition proceedings."
FIFA has insisted it will continue to co-operate with the US investigation.
"FIFA became aware of the actions taken today by the US Department of Justice," world football's governing body said in a statement.
"FIFA will continue to co-operate fully with the US investigation as permitted by Swiss law, as well as with the investigation being led by the Swiss Office of the Attorney General."
Thursday's developments started early with police arriving at the Zurich hotel with FIFA officials present ahead of a two-day ExCo meeting to vote on reforms within world football's governing body.
With Hawit and Napout having been taken away, the FOJ released a statement, which read: "The detention orders issued by the FOJ are based on arrest requests submitted by the United States Department of Justice on 29 November 2015. In the light of further investigations conducted by the United States Attorney's Office for the Eastern District of New York, these individuals are now also suspected of having received bribes.
"The high-ranking FIFA officials are alleged to have taken the money in return for selling marketing rights in connection with football tournaments in Latin America, as well as World Cup qualifying matches. According to the arrest requests, some of the offences were agreed and prepared in the USA. Payments were also processed via US banks."
The detentions follow previous police actions in May, when seven FIFA officials were arrested for alleged racketeering, conspiracy and corruption.
Two of the seven agreed to simplified extradition proceedings. Jeffrey Webb - who held the role at the top of CONCACAF in between Hawit's two terms - and Jose Maria Marin were then transferred to the US authorities on July 15 and November 3 respectively.
However, the other five - Eugenio Figueredo, Eduardo Li, Julio Rocha, Costas Takkas and Rafael Esquivel - opposed their extradition to the USA, and their appeals against the FOJ's rulings are pending before the Federal Criminal Court.
The events in May eventually led to Sepp Blatter's decision to step down as FIFA president just days after winning a fifth term in charge of the governing body, with a new president to be elected on February 26, 2016.
Blatter has since been hit with a provisional 90-day ban from all football-related activities by FIFA's ethics committee after a criminal investigation was opened into allegations he sold a World Cup TV rights contract to former FIFA official Jack Warner in a deal that was unfavourable for FIFA and that the 79-year-old made a disloyal payment of two million Swiss francs to Michel Platini, with the Frenchman and secretary general Jerome Valcke also receiving provisional bans following the corruption claims.
Issa Hayatou, who heads the Confederation of African Football (CAF), is the acting FIFA president during Blatter's ban, but will not stand for election during February's vote.
Jerome Champagne, Gianni Infantino, Sheikh Salman bin Ebrahim al-Khalifa, Tokyo Sexwale and Prince Ali bin al-Hussein are due to run for the presidency early next year.