Vice-chancellor Saleem Badat was addressing the municipality on Wednesday in an open letter.
University staff and students marched to the Makana municipal offices to protest the continued lack of services.
Service delivery in the Eastern Cape, one of South Africa's poorest provinces, continues to be a problem.
Last year, Parliament's public service and administration committee heard that the province had a R42-billion service delivery backlog.
"Since August 6 2013 and for the past nine days, parts of Rhodes University, including 11 residences that house over 1 000 students and wardens, have been without water.
"As this open letter was being written yesterday [Tuesday] afternoon, 35 additional residences and various other parts of the university were also without water," he said.
It was later announced by dean of students Vivian de Klerk that the water problem had extended to more than 40 residences and the thousands of students they house.
De Klerk mentioned measures that the University was taking during the crisis, stating that:
• 2 litres of drinking water are available per student per day at all dining halls at meal times
• Water is being provided to as many residences as possible for the flushing of toilets
• All tanks on campus are being re-filled daily
• wet wipes are available for hygiene purposes
• the University is monitoring the impact of the lack of water on student health, and there is currently no cause for concern.
• we [the University] are investigating the provision of waterless toilets in key areas
No shower or laundry facilities were available, she said.
Badat said that in March this year, the university was also without water, despite the fact that it pays R2.5-million in rates to the municipality every month.
"Now, once again, we are faced with the crisis of hundreds of our students and staff without drinking water, which the university has to supply. There is no water for personal ablutions, for cleansing, for flushing toilets. Conditions in the residence toilets are dire, with growing health concerns.
"We are again on the brink of having to close the university. Despite the valiant efforts of our staff and the great fortitude of our students we cannot cope any longer.
"Can you at all imagine the chaos that will occur if the university has to close its doors? Or the economic impact that this will have on the town, which is highly reliant for its economic wellbeing on the university operating?
"It is time for you, our municipal leaders, to demonstrate leadership and accountability to us, your constituents, and to give your full attention to the problems of basic services that are crippling our town and compromising the promise of a better life for all," said Badat.
The letter was also sent to minister and the director general in the department of higher education and training.