Marvin Rees said that the proposals were progressing, with ecological reports carried out and funds allocated for an outline business case.
The idea of an underground system was raised in 2017, but critics labelled the idea "pie in the sky" and warned of escalating costs.
Mr Rees said the city council would work with the government on funding.
Speaking during a Facebook Live event, the mayor said the proposals were "moving on" but it was not a scheme that could be completed quickly.
"You can't dig a hole until you have a plan, until you know if you're going to go down a £4bn scheme," said Mr Rees.
"It has to add up financially, and you don't want to get in a tunnel that's going to cave in, so experts will do their job with all the paperwork at the beginning."
The prospect of underground rail is hinted at in the West of England Combined Authority's (Weca's) draft Joint Local Transport Plan. It has identified four major routes for a mass transit system for the Bristol area, serving Bristol Airport, Cribbs Causeway, east Bristol and the A4 corridor to Bath.
Funds have been allocated for a business plan which will be assessed by the Department for Transport next spring, said the mayor.
Mr Rees said the mass transit system was a "central plank" of the council's transport plans and would provide a "viable alternative to private cars".
A Weca spokesperson said: "A new high-capacity, fast and reliable public transport network could lead to significant numbers of people leaving their cars behind, resulting in lower carbon emissions and better air quality."
source: BBC News
A £4bn project to create an underground rail network in Bristol is still in the pipeline, says the city's mayor.