Several hundred staff at the World Health Organization (WHO) headquarters in Geneva have taken part in a one-hour stoppage over job cuts.
Mr Lee warned staff against taking part in the stoppage
The UN body's employees took part in the action despite being warned they could be fired for doing so.
WHO spokeswoman Christine McNab said fewer than 400 staff out of 2,400 had taken part. The body representing WHO staff said up to 700 had participated.
Ms McNab said the WHO was deciding what action if any to take against them.
The Director General of the WHO, Lee Jong-Wook, had said the action risked undermining the organisation's credibility at a critical time for global health.
An official in the body representing WHO employees said Mr Lee's letter was a form of intimidation and violated workers' rights.
The WHO plans to cut between 200-300 jobs at its headquarters.
However, the increased use of 11-month contracts is also a source of discontent.
Each WHO employee is allowed only four of them; after 44 months they must be taken on permanently or let go.
That 44-month deadline is approaching for many people and the fear is that job losses could be widespread, says the BBC's Imogen Foulkes in Geneva.
A strike there is unprecedented, and the fact that it was held is a reflection of deep dissatisfaction among some staff, our correspondent adds.