In the last six months, three employees have killed themselves at work.
The most recent, a 42-year-old executive, left a note complaining that "for three years, I have the impression of being harassed and cornered by my superiors."
An unofficial list by employees alleges there have been five suicides and one attempted suicide sine January alone.
These are in addition to eleven suicides in 2011 and 17 in 2010.
La Poste is eager to avoid the fate that hit France Telecom where more than 60 employees were believed to have committed suicide over a three-year period due to work pressures.
The controversy forced deputy chief executive Louis-Pierre Wenes out of his job in 2009.
On Monday, the head of La Poste, Jean-Paul Bailly, announced four measures he hopes will help the situation.
"A big dialogue around work" will be launched, he said, as well as a series of discussions with unions to put in place "concrete measures."
A mediator will also be appointed who can take decisions on individual situations.
However, unions were disappointed that the measures did not include a suspension of the company's ongoing reform programme.
"The transformation of the company cannot stop," said Bailly. "There will not be a pause."
Unions reacted angrily to the news.
"We are sceptical about these measures," Bernard Dupin of the CGT union told newspaper 20 Minutes.
"We wonder if management has really taken account of what's going on in the organisation."
The SUD-PTT union denounced "four miserable little measures" in a statement and said it would go directly to the government, major shareholder in La Poste.
The union said the government "could not stay silent" on the matter.