If inspectors are to be involved in school closures, they will need to be trained and their numbers increased, councils have warned MSPs.
Local authorities have also voiced concern over plans, contained in planned legislation, to give Scottish ministers the power to "call in" a school closure proposal, thereby taking it out of the hands of the local authority. Firm criteria needed to be established to ensure "consistency", they said.
Bruce Robertson, Aberdeenshire Council's director of education, learning and leisure, said the School (Consultation) (Scotland) Bill, which the Parliament's education committee is currently scrutinising, lacked "substance and clarity" on this issue.
Edinburgh City Council, meanwhile, wanted ministers who decided to call in a school closure to be subject to a time limit to avoid authorities and schools being left "in limbo".
"Previously, we've been aware it does take a considerable amount of time to get a decision," said Lindsay Glasgow, asset planning manager in the council's children and families department.
If the bill was passed, it would require councils looking to close schools to consult on closures for at least six weeks during term time, hold a public meeting and seek the independent view of HMIE.
However, in evidence to the Parliament's education committee last week, local authority managers and the Association of Directors of Education in Scotland all stated the inspectorate would be unable to cope with the additional responsibilities.
In written evidence, Glasgow City Council went further, saying that the involvement of HMIE was "inappropriate" and went beyond "their capacity, function and area of expertise". It had the potential to "undermine local democratic processes", the council said.
However, in oral evidence last week, Glasgow made a U-turn. Jim Wilson, head of performance and asset management, said the authority was becoming "much more comfortable" with the proposal as the role of HMIE became clearer. Like other councils, he said, its only concern now was over HMIE's "capacity" and the additional resources it would require.
Mr Robertson said: "We have concern over how well placed HMIE is to ensure consistency of approach in evaluating these matters. Some enhanced capacity in the organisation would be needed."
Angus Campbell, Western Isles Council leader, said he was also comfortable with HMIE's new role. However, he criticised the inspectorate for its "complete change of tack" over his authority's plans to close four S1-2 schools.
Education Secretary Fiona Hyslop rejected the council's plans earlier this year after HMIE advised there would be "no educational advantage" to closing two of the schools. Previously, however, HMIE had criticised councillors for their delay in closing schools and commended them for finally deciding to shut the small secondaries.
Mr Robertson, for his part, said he found ministers' recent refusal to approve the closure of Cabrach Primary in Moray, which has two pupils who are siblings, "very concerning".
When school rolls dropped to single figures, he added, it was difficult to give pupils "a rounded set of experiences".