Police deployed officers and staff to check nearby public places, tourist attractions and hotels. Details of the boys were circulated to public transport operators and Solent ferry companies.
An address given for the family on the Isle of Wight was checked by officers. The details provided were found to be incorrect.
The force is keeping an open mind about the circumstances of this report. There is no evidence at this time to confirm a criminal offence has been committed deliberately. There could be a completely innocent explanation for what happened.
We are renewing an appeal for the parents or any relatives of these two boys to contact the police."
More top news
A court has heard how 13 year old Alexander Worth was killed when a high-performance Ferrari F50 crashed on a farm track in Hampshire.
Monday evening's weather for the west of the region
Monday evening's weather for the east of the region