She would, however, co-operate with the auditor general and the public protector on an investigation into the tender process to buy the plane, her office said on Tuesday.
Spokesperson Ndivhuwo Mabaya said: "No information would be provided to the Democratic Alliance (DA) and there is no basis in law for the ministry to do so".
He was responding to the DA's challenge to Sisulu that she produce proof that the tender process was sound.
Earlier DA parliamentarian David Maynier said: "Sisulu should produce documentary evidence that the minister of finance, Pravin Gordhan, approved the deviation from normal competitive bidding processes."
Mabaya said: "It is our suspicion that the DA is demanding this information in order to parade it in the media but not for oversight and monitoring of the work of the department."
He said the party was ignorant of the government's procurement processes, as ministers were not responsible for buying but were mandated to create "an enabling environment".
This included submitting the project to Cabinet and consulting with the finance minister.
Rather, accounting officers, director generals and chief financial officers were responsible for rolling out procurement processes.
Mabaya appealed to the DA to let the public protector and auditor general's investigations unfold.
On Monday, Sisulu said she was "absolutely convinced" the department had followed correct procurement processes regarding the R2-billion Boeing 777-200 Long Range business jet.
She said the defence department had taken advice from national treasury as well as the accountant-general on the potential purchase, which had been making headlines since the weekend.
On Monday Mabaya said she had called for the deal to be suspended to allow her successor at defence, Nosiviwe Mapisa-Nqakula, to redefine the department's priorities.
'Matter of national security'
Maynier also took issue with this step, calling it an attempt to distance herself from the matter.
"This sounds too much like a useful pretext to extricate herself from a dubious deal to purchase a new jet for President [Jacob] Zuma," he said.
Die Burger newspaper reported that Sisulu had planned to use a R3.5-billion refund the government had secured on the cancelled purchase of eight A400M Airbus military transport planes to buy the new jet.
According to the daily, Sisulu wrote to Gordhan last month, asking to be exempted from the normal tender rules because buying a new plane for the president was a "matter of national security".
Maynier said if Sisulu produced documents to prove that Gordhan approved the deviation from the normal bidding process, he would withdraw his request that the public protector investigate the matter.
Both the DA and the Inkatha Freedom Party said it was unconscionable that the government would spend that much on a presidential jet when so many South Africans lived in poverty.
"This money could be better spent in trying to alleviate the many burning issues our country faces, such as our socio-economic challenges," IFP spokesperson Albert Mncwango said. – Sapa