It would also allow polytechnics and wananga to call themselves universities if given permission.
"We are strongly opposed to this provision because we believe it represents a threat to the international reputation of New Zealand's universities," Universities New Zealand said in its submission.
Wanangas and polytechnics were distinct from universities and their respective labels provided clear signals to students and employers, both in New Zealand and overseas, about the sort of education provided.
The concern was backed by Otago University vice-chancellor Prof Harlene Hayne in its submission on an earlier version of the Bill.
"Any dilution of this standard would undermine the overall reputation of New Zealand universities internationally, blurring the line between our highly regarded universities and other parts of the tertiary sector, some of which have been involved in or associated with practices that have been damaging in an international context.
"This is a particular concern at a time when the recruitment of overseas students in an increasingly competitive international market is a high priority for both the university sector and the country as a whole," Prof Hayne said.
Universities New Zealand was also worried a provision aimed at "equal treatment of all tertiary education providers".
"For example, a degree taught in a research-rich environment and a degree of the same name taught in an environment largely devoid of research will not be of the same quality, nor create the same outcomes."
Dunedin Tertiary Education Union representative Kris Smith said the Bill would make it easier for the Government to move public funding into private institutions.
Private institutions regularly put profits before paying staff reasonable wages and offering good conditions.
This was not conducive to "providing quality education".
She also feared private institutions funded by the Government could abandon smaller communities for larger cities, leaving people in rural areas with no access to local training.
It would mean funding would become unpredictable and focused on short-term outcomes, not long-term stability.
Instead of focusing on quality education, tertiary institutions would fight among themselves for funding and enrolments.
Tertiary Education Minister Paul Goldsmith said wananga would have to meet criteria before being given permission to use the "university" term.
He said he would read the select committee report based on the submissions received on the topic with interest.
The Bill merely put into the law the Government's policy of funding private and public providers equally, introduced five years ago.
