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.

Mr Gargan, 48, was found guilty of eight charges of misconduct but has been allowed to return to work.
The Avon and Somerset branch of the federation said it "cannot envisage" how the public or police can have "confidence in his leadership".
Mr Gargan said he understood people had questions and said he would address these.
In a statement issued through the Chief Police Officers Staff Association, he said he was "very much looking forward to returning to work" and "beginning the process of rebuilding confidence in the force".
The comments about his return to work were made in an open letter to Avon and Somerset Police and Crime Commissioner Sue Mountstevens.
Mr Gargan was suspended following allegations of data protection breaches and inappropriate behaviour with women.
A panel found him guilty of misconduct - but cleared him of gross misconduct. His suspension was lifted and a phased return to work prepared.
Mr Gargan said his actions had "fallen below the standards expected of a chief constable".
In the letter seen by the BBC, the Police Federation said the chief constable is "the person that sets the standard of professional behaviour and ethical conduct" and the role "must be beyond reproach" in the eyes of the public and police officers.
It said its officers had been asked on a daily basis by "the communities they serve" how the chief constable "can return to work in these circumstances".
The letter ends with the federation calling on the commissioner to "show strong leadership in dealing with this issue".
Some former members of the force have also criticised Mr Gargan's return.
One group of retired officers said the "debacle" had caused "more pain and damage to morale than is imaginable".
Lawrie Lewis, a retired Chief Superintendent, said the force's reputation had been "severely tarnished".
Sue Mountstevens said: "The procedure to be followed in relation to the sanction hearing is strictly regulated.
"As with all judicial processes when proceedings are not complete it is not possible to discuss or comment upon them until they have been finalised."
Plans to ban the use of e-cigarettes in enclosed public places have divided a group of AMs looking at the proposal.
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The Police Federation has expressed a lack of confidence in Avon and Somerset Chief Constable Nick Gargan.