In a letter, the firm rejected the minister's concerns about media plurality and broadcasting standards.
It also said she had based her view on "seriously flawed" evidence.
But it welcomed "a thorough" review and said it would work with regulators.
"21st Century Fox is confident that the transaction will be approved based on an objective assessment of the facts," said Jeffrey Palker, executive vice president at the firm.
Ms Bradley has been weighing up whether to refer the deal to Ofcom after warning it could pose "public interest considerations" that warranted further investigation.
One concern is that the merger would give businessman Rupert Murdoch too much control over the British media landscape. He also said her "provisional view" of the deal was based on a flawed report about media plurality, prepared by campaign group Avaaz and the Media Reform Coalition.
He said: "These flaws include the misattribution of consumption of news on commercial radio to Sky... the erroneous characterisation of News Corp as the 'largest newspaper provider' and inaccurate claims that rising online readership has 'eclipsed' the dramatic decline in circulation of News Corp titles." This is because both Sky and Fox are controlled by Mr Murdoch, who also owns News UK, publisher of the Times and the Sun newspapers.
But in the letter, Mr Palker said the minister had not fully taken into account 21st Century Fox's decision to spin off News Corp in 2011.
He also said her "provisional view" of the deal was based on a flawed report about media plurality, prepared by campaign group Avaaz and the Media Reform Coalition.
He said: "These flaws include the misattribution of consumption of news on commercial radio to Sky... the erroneous characterisation of News Corp as the 'largest newspaper provider' and inaccurate claims that rising online readership has 'eclipsed' the dramatic decline in circulation of News Corp titles."
Ms Bradley also questioned whether the proposed deal threatened broadcasting standards, singling out "corporate governance failures" at News Corp during the phone-hacking scandal of 2011 as a cause for concern.
But Mr Palker said 21st Century Fox had transformed its corporate governance since that time.
"In fact, the level of scrutiny and controls we have imposed around the world were informed by the lessons learned in 2011," he said.
A decision to intervene would not block the deal, but trigger an Ofcom assessment as well as a Competition and Markets Authority report to be considered by Ms Bradley.
The European Commission could also choose to examine the deal if it has competition concerns.
21st Century Fox is offering £11.7bn for the 61% stake in Sky it does not already own, valuing the entire company at £18.5bn.
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