Ramaphosa, who took power in February, expressed "serious concern" over the clashes between police and protesters, and called for calm as he faced one of the first major challenges of his presidency.
Following their meeting, he pleaded with the residents for time to come up with a solution, after consultations with the community and entire North West Province.
Ramaphosa arrived in the city on Friday and was locked in talks with local leaders after he cut short his trip to a Commonwealth summit in London.
He called for people "to express their grievances through peaceful means and engagement rather than violence and anarchy" and urged security forces to show restraint.
Public healthcare in the province was brought to a grinding halt by the National Health Allied Worker's Union's (Nehawu) almost two-month industrial action, a strike in some parts and a go-slow in others, which left clinics and hospitals in the province without medication or personnel.
The latest protests erupted on Wednesday with residents demanding that the province's Premier Supra Mahumapelo, a member of Ramaphosa's ruling African National Congress party, step down.
"We are doing our best to keep the situation under control", police spokesman Sabata Mokgwabone told ENCA television.
South Africa's foreign minister, Lindiwe Sisulu, confirmed that Botswana had closed its border with the province because of the chaos, SABC reported.
The South African Military Heath Service (SAMHS) have been deployed to the North West to reinforce the medical care capacity at the Provincial Health Hospital.
The party and its leadership also face internal divisions after the tumultuous resignation of former President Jacob Zuma in February after multiple scandals and allegations of graft.
Unemployment is at a record high of about 28 percent, with youth unemployment reaching over 50 percent in many areas.