Venables said the BBC television program Panorama, which contained allegations about his dealings surrounding the 1991 takeover of Tottenham Hotspur, was "grossly deficient in every area of its investigations into my affairs."
"There are few people who have no enemies but I am unfortunate in that the few people with whom I have fallen out are well-placed to undermine me," he said in a statement.
"I wish to assure all the people who have supported me through another difficult time that I will bounce back from this disgraceful character assassination and will begin the task immediately," said Venables, who was appointed national coach in January.
Graham Kelly, chief executive of the FA, said Venables remained the right man for the job. The allegations about Venables were unproven and did not affect his ability to coach the national team, he added.
"The program presented no evidence to cast doubt on his qualifications to be the England football coach or on his capacity to do the job," Kelly told a press conference.
The FA appointed Venables to replace the sacked Graham Taylor after Panorama had first queried financial aspects of Venables's takeover of Tottenham.
"Crucially, it is our belief he retains the overwhelming backing of his fellow professionals to fulfil the task he's undertaken," Kelly said.
"He will continue to do so with the FA's full backing."
Venables issued a writ against Panorama for its first program. In Tuesday's statement, he indicated he was preparing to take the same legal recourse.
Panorama made a series of allegations about the financing of Venables' takeover of Tottenham and alleged financial sleight of hand enabled him to avoid paying huge court costs to his former partner, Alan Sugar.
Venables was sacked as Tottenham's chief executive by Sugar, chairman of the Amstrad computer and consumer electronics firm, in May 1993. Sugar was brought in to save the club from financial ruin on Venables' insistence two years earlier.
Venables failed in his court bid to claim wrongful dismissal and costs were awarded against him.
On Saturday, Britain's Serious Fraud Office (SFO) said it was examining Venables' affairs following an investigation by the Department of Trade and Industry (DTI).
Panorama claimed the DTI probe had found evidence of wrongdoing that could lead to Venables' disqualification as a company director.
Venables said he had never been informed about the DTI findings. "The SFO have confirmed to me that they have no plans to bring charges against me."
In a statement Monday, Venables said he had committed no crime: "My position remains as before -- that I have done nothing dishonest, I have nothing to fear from this program and that it is just another step in a bitter campaign to discredit me."
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