Earlier Thursday, Thaksin told reporters that the Asian nation was not taking advantage of Kenya to get the wildlife.
"Those who are criticizing (us) without knowing will feel sorry for what they are doing," he said before leaving for Turkey.
"We are not coming to take advantage of Kenya. We are developing countries. We have sympathies for each other. Everything will go according to the law and international principles, please understand that," he added.
The spokesman said a timeline for the relocation of animals to the soon-to-be-opened Mae Hia Safari Park in Thailand's northern Chiang Mai province had not been set but experts were working on the details.
In addition, Mutua rejected earlier claims that Thailand was offering expert elephant trainers and $1 million (1.2 million euros) to boost conservation in the country.
"Thailand is not paying for any of the animals. However, the translocation and upkeep of the animals is being conducted at Thailand's expense and according to international laws and safety," he said.
The deal, signed on Wednesday, "is open-ended and it is in our interest to ensure that all animals are safe and healthy. If any animal is experiencing difficulties, we will be able to work with it and even return it back home," Mutua told reporters.
