The southern African nation's economy stagnated last year, fanning anti-government protests and compounding President Robert Mugabe's problems ahead of national elections due in 2018.
Public sector workers are paid an annual bonus equivalent to a month's salary every November and December, but the government - which spends more than US$250 million monthly on salaries - has not said when it will make the 2016 payment.
Owning residential land is sees as unattractive as most plots lack basic amenities such as roads, electricity and sewerage, making them difficult to settle on or sell.
Raymond Majongwe, secretary general of the Progressive Teachers Union of Zimbabwe, described the government's offer as
"madness" and said unions rejected it at a meeting on Wednesday.
Unions also turned down a second offer to pay half the bonus in cash and the rest in "non-monetary" benefits that the government did not spell out.
"The government should just pay what is due to the workers and not cry about financial problems," Majongwe said.