Eriksson told an undercover News of the World reporter - posing as a rich Arab - he would quit as England coach if they won the World Cup, and suggested he would be prepared to become manager of Aston Villa as part of a takeover bid.
The Swede also made indiscreet comments about his own players, just a few days after he stressed the importance of creating the right "ambience" in the squad when took over from Kevin Keegan five years ago.
However in a statement Sunday to the official website of the FA - Eriksson's employer, the 57-year-old said: "I would like to assure everyone, especially the fans, that I'm 100 percent committed to the England job. I've told the FA this and I value the great support I have received from them."
And with the World Cup finals getting under way in Germany in June, Eriksson insisted his standing with his squad had not been affected by the News of the World report.
"I have spoken with the players concerned today and I have been very pleased with their reaction and am confident my relationship with them has not been damaged in any way."
In the News of the World report, the Swede was quoted as discussing key members of his squad.
"He is lazy sometimes," Eriksson said of Manchester United centre-back Rio Ferdinand.
He then referred to Ferdinand's United team-mate Wayne Rooney, describing the player as having a "temper" and "coming from a poor family".
Eriksson said David Beckham was "a bit frustrated" at Real Madrid and offered to phone the England captain to persuade him to return to English football with Villa.
And he is also reported to have commented on the position of England striker Michael Owen, who joined Newcastle in a 17-million-pound transfer from Real Madrid in August after a deal could not be struck with his former club Liverpool.
The FA said Eriksson had their support.
"Following reports in today's News of the World, the Football Association can confirm that England head coach Sven-Göran Eriksson continues to have the full support of the organisation," the FA said in a statement.
"This follows conversations between FA chief executive Brian Barwick and Sven, and subsequent conversations involving Brian with FA chairman Geoff Thompson, international committee chairman Noel White and senior FA figures."
Meanwhile Newcastle responded to Eriksson's comments about Owen.
The England coach reportedly said: "I talked to Michael Owen and said, 'You are happy?' He said, 'Not really with the club, but economically I never earned that money in my life'. So they paid a higher salary than Real Madrid did."
But Newcastle chairman Freddy Shepherd countered: "We have spoken with the player and he has confirmed he is happy at Newcastle United."
Earlier Eriksson's agent, Athole Still, insisted the former Lazio manager wanted to extend his current England contract by a further two years to 2010.
"Sven said to me quite recently 'perhaps I've got used to this job despite the annoyances of it - perhaps you should have a word with Brian Barwick and see if the FA would be interested in me staying until 2010'."
The News of the World's revelations add to a growing list of unflattering headlines featuring Eriksson in off-field incidents.
Secret meetings with Chelsea chief executive Peter Kenyon left the FA in an awkward position as Eriksson appeared to be lining up a lucrative job at Stamford Bridge.
FA officials responded with declarations of support and an improved contract.
The Swede hit the headlines again when details of an affair with FA secretary, Faria Alam, who had also had a relationship with then FA chief executive Mark Palios.
The fall-out when the affairs were made public saw Palios and Alam both quit the FA.
His personal life also came under scrutiny when television personality and fellow Swede Ulrika Johnson revealed the two had an affair in 2002 ahead of the World Cup in South Korea and Japan.