However, the easing will be applied only on public transport modes involving less than 50 minutes of travel such as buses and city rail systems, while commuters will still have to wear face masks.
Saksayam cited medical findings that the chances of catching Covid-19 were zero for commuters who sat together, wore masks and did not take trips of more than 50 minutes.
The findings had prompted the government's Centre for Covid-19 Situation Administration to consider easing the social distancing rules, he added.
Transport modes with travel times that exceed 50 minutes, such as trains and tour buses, will still have to adhere to social distancing rules.
Saksayam has instructed state transport agencies to complete new guidelines on social distancing by next week, covering measures such as signs explaining that friends and families can sit together.
He expects the relaxation of social distancing to begin on July 1.