Pupils should have started at the £5m Primrose Hill Primary in Ordsall, Salford, this week.
But parents were told the opening was to be delayed due to workmen still being on site.
They were first told the opening had been put back from September 5 to September 10, but they have now been told children cannot start until September 17.
Salford's education boss, Coun John Warmisham, said: "The school has not been finished on time. For health and safety reasons, we cannot allow children into the building when there are still workmen on site.
"I understand the contractors had problems with getting basic services connected.
Penalties
"We are disappointed the school is not ready and will look at the possibility of the contractors facing financial penalties for not delivering it on time."
The 280-pupil school is to replace two other estate primaries, St Clement's C of E and Radclyffe, which have closed.
One local resident said: "This is a major mistake by the council. They have closed two perfectly good primary schools and then can't even get the replacement ready on time.
"There has been no alternative provision made for the children. I think it's despicable. It wouldn't have been allowed to happen anywhere else."
The £5m school has been built by Warrington-based contractors Cruden. The work started on April 3 and was due to have been finished by July 27.
Salford council says that `unforeseen ground conditions and significant issues with utility companies to provide power and water' had caused delays.
Cosmetic work finishing off the interior and landscaping still needs to be done.
Coun Warmisham said: "We've been ringing round parents to apologise and explain what has happened.
Conditions
"Difficult ground conditions made the work take longer than expected and the knock-on effect put other aspects of the build behind schedule."
Sheryl Moor, whose sons, Kane, seven, and Kade, five, were due to start at the school this week, said: "They have been off school for eight weeks and are bored out of their minds.
"We've been told the school will be ready on September 17, but I'm not convinced.
"I'm furious. I've made an appointment with St Josephs RC Primary. I'm thinking of having the boys christened and getting them in there."
Another parent, Collette Hamey, said: "I think we're being fobbed off again." Tweet

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"think I'll get them christened and get them in there" - that'll sort everything out won't it - just like that!
To the lady who is thinking of having her sons christened to get them into St Josephs. The whole idea having your child christened is for religious reasons not to get them back to school quicker because unfortunatly their school is not ready yet.
Read this & imagined the childcare bill some of the parents must be facing!?