The software company says its South African operations paid "commissions" to Gupta-linked companies for contracts with SOEs.
The Chinese ambassador reportedly met the Guptas, as a dodgy Transnet tender with a Chinese company was negotiated.
The UK says it is taking the allegations seriously.
Lord Peter Hain says South Africa is gripped by a political, economic and social crisis.
Committee members felt Zwane failed to respond to a number of their questions and resolved to schedule another meeting with him to continue the probe.
The investigation is reported to draw on information from masses of emails leaked from within the Gupta corporate empire earlier this year.
The Hawks say they do not have access to the full #GuptaLeaks cache of documents.
A series of reports, letters and emails seen by amaBhungane and Scorpio suggest the contract never came into force.
A whistleblower says the Gupta-linked firm gave access to government officials to international consultancy firms for a fee.
They helped 75 schools and created jobs, said the home affairs minister.