The organisers of the Keep Our Assets petition are confident the signatures delivered to Parliament will force a referendum on asset sales.
About 150 people attended a rally at Parliament to hand over 70 boxes containing the petition, and 392,000 signatures.
They were met by Opposition MPs including Green Party co-leaders Metiria Turei and Russel Norman and Labour leader David Shearer.
One of the petition organisers, Grey Power President Roy Reid, told the rally he's sure there will be the 304,000 valid signatures needed to force a referendum on the sale of state owned assets.
He says his generation worked hard and paid the taxes to build the assets, and they are not for sale.
Prime Minister John Key says a huge number of signatures will not be genunine and will have to be struck off.
The numbers registering interest in buying shares in Mighty River Power have reached 290,000.
Speaking in Brazil during his 10-day visit to Latin America, Mr Key said the Mighty River partial sale was proving at least as popular as the opposition's petition.
The Clerk of the House has until 12 May to check if at least 10% of registered voters have signed the petition.
If that threshold is reached, the Government will have one month to name a date for a referendum but can delay a vote for up to a year.
Finance Minister Bill English says the Government respects the petition process but will stick to its plans.
Mr English says referenda are not binding and he says the Government won a mandate for asset sales at the last election, and will not change its plans.