David Rees, who chairs the assembly's health committee, said it was "unable to reach a consensus view" on the idea.
The five Labour members supported curbs on e-cigarettes, claiming their use "normalises" smoking behaviour.
The idea was opposed by four opposition AMs, while Plaid Cymru's Elin Jones suggested imposing less stringent restrictions than those on tobacco.
As the Labour Welsh government does not have an outright majority in the Senedd, it will need some opposition support to get the measure passed as part of the Public Health (Wales) Bill.
The plan, intended to come into force in 2017 and the first in the UK, has divided opinion among health and medical groups.
Some anti-smoking campaigners have opposed restrictions, saying e-cigarettes help smokers kick the habit.
But Health Minister Mark Drakeford has said it is a "balance of risk", claiming restrictions on e-cigarettes will deter children from smoking.
In a report on Monday, the committee said it agreed with the bill's other proposals, including a licensing scheme for tattoo and piercing parlours, and a ban on intimate piercings for under 16s.
Plans to ban the use of e-cigarettes in enclosed public places have divided a group of AMs looking at the proposal.