Zaid al-Hilli told ITV News that his family was "very encouraged" by the arrest made in the investigation into the death of his brother and his family.
"We are very encouraged by the recent developments. Hopefully we will get to the truth," he said.
But he added: "I don't want to raise my hopes."
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Tory Eurosceptic Jacob Rees-Mogg played down the significance of the deal struck by the Government to win over pro-EU rebels.
The Tanaiste issued the warning to the UK ahead of a visit to Dublin by European Commission President Jean-Claude Juncker.
Around 9,500 people gathered at the neolithic World Heritage Site to attend the overnight celebration of the longest day of the year.