Eleuterio Huidobro told Reuters news agency that Uruguay had not imposed or accepted any conditions when it agreed to receive the former inmates.
The six men arrived in Montevideo on Sunday after being freed by the US.
They spent 12 years in prison for alleged ties with al-Qaeda but were never charged.
The former inmates - four Syrians, a Palestinian and a Tunisian - were taken to a military hospital for health checks.
|Montevideo Military Hospital|
Uruguayan President Jose Mujica said they had been subjected to "an atrocious kidnapping".
"They will not be restricted in any way. Their status is that of refugees and immigrants," he told Reuters.
|Uruguayan President Jose Mujica|
Mr Mujica has spoken out against the Guantanamo Bay detention centre
About half of the 136 men still in Guantanamo have been cleared for transfer but have nowhere to go because their countries are unstable or unsafe.
In Latin America, El Salvador is the only other country to have given Guantanamo prisoners sanctuary, taking two in 2012.
|Guantanamo Bay Detention Facility|
"Were it not for Uruguay, I would still be in the black hole in Cuba today," he said.
"I have no words to express how grateful I am for the immense trust that you, the Uruguayan people, have placed in me and the other prisoners by opening the doors to your country."
Mr Mujica was himself held for over a decade in harsh prison conditions during Uruguay's period of military rule in the 1970s and 1980s.
He made the decision to take detainees from Guantanamo in March but the move was delayed until after November's presidential elections.
He was constitutionally barred from seeking re-election, but the vote was won by his party's candidate, Tabare Vasquez, who begins his term in March.