The cash-strapped City of Tshwane owes Eskom R1.9-billion.
Eskom said on Wednesday the metro had underpaid by R179-million on its April invoice, and the May invoice of R776-million still needed to be paid.
The total debt owed by the municipality to the power utility had grown to just under R1.9-billion as of 9 June.
Eskom said it had made various attempts to engage Tshwane on the growing bill - and it has now publicly appealed to the metro to pay the debt.
The company has not ruled out approaching the court for relief.
"The power utility has appealed to the City to settle the March and April 2023 invoices immediately and to pay its monthly accounts on the due date. Eskom does not have the financial capacity to continue supplying bulk electricity to the City without the necessary payments," Eskom said.
"As Eskom's cash flow challenges and the provisions of the PFMA dictate, Eskom is accordingly exploring all avenues available to it to recover this debt, including, but not limited to, approaching the courts for relief," said Mpumelelo Mnyani, the senior manager for customer services in Gauteng.
Tshwane has long suffered from financial problems, and it recently passed a budget which was presented despite being underfunded.
In response to Eskom, the office of the mayor, Cilliers Brink, said the City was working on increasing its revenue collection from businesses and residents who needed to pay for services.
The City was targeting 1 000 customers per day and following up on their non-payment.
"Tshwane's mayoral committee is not in denial about this situation, nor do we deny that we owe an obligation to Eskom, which we have to pay," said Sipho Stuurman, Brink's spokesperson.
"The mayor is on record that getting control of the City's finances, and responding to the findings of the AG, two interrelated matters, constitute the City's number one political priority.
"To this end, National Treasury has deployed resources to Tshwane and has had direct input into the budget adopted by the City for the 2023/24 financial year.
"Difficult measures have been taken in terms of this budget, including the decision not to budget for salary increases for employees and councillors.
"As the mayor announced in his State of the City Address, far more rigorous attempts are being made than in the immediate past to strengthen the City's revenue value chain."
Eskom has long complained about the non-payment of debt by municipalities.
The power utility had previously approached the courts for orders against delinquent councils.
The company was in November 2022 awarded a court victory to attach R1.3-billion of assets belonging to the Emfuleni Local Municipality in Gauteng.