Mexican authorities have dropped a criminal investigation over allegations that six Britons rescued from a cave were searching for uranium.
But the men, who were on a military training expedition, were continuing to be held over possible visa irregularities.
Immigration officials have until Monday to interview the men before they must decide whether to take further action.
An MoD spokeswoman said: "They saw the Attorney General yesterday and they were released without charge but now the Mexican authorities still have them."
But the army's most senior officer Chief of General Staff General Sir Mike Jackson, said the cavers' difficulties had simply been the result of a "great misunderstanding" and the purpose of their expedition was to "bolster initiative and courage".
He told BBC1's Breakfast with Frost: "It seems to me that their purpose was to explore these caves further than they had already been explored. There seems to be a misunderstanding. I very much hope it gets sorted out quickly."
The five servicemen and their civilian guide were rescued from a waterlogged cave on Friday after spending more than a week underground.
They were initially questioned over visa issues and later police investigated local media reports that they had been looking for radioactive materials - claims repeatedly denied by the Ministry of Defence and now dropped altogether.
It is now up to immigration officials to decide if they broke the terms of their tourist visas.
They could be deported, barred from returning for several years, face fines of up to £180 or jailed for 18 months if found to have broken immigration rules.