Yesterday, Vaz was strident as he responded to questions from journalists during the post-Cabinet media briefing at Jamaica House.
"This matter has been put properly before the minister of justice and the attorney general's department," Vaz told journalists. "It is a case for them to deal with. They have it in front of them and it is being actively pursued."
He added: "The question of making a call for the prime minister's intervention smacks of politics. The fact of the matter is that there has been no extradition in previous times that has had any intervention or comment of a prime minister."
He said the extradition request was being dealt with through the protocols established and a decision would be publicly stated when one has been made.
"And no amount of calls, either by private sector or opposition, is going to rush that process," declared Vaz.
Increasing criticism
Golding has been facing increasing criticism over his silence on the extradition request which was made public more than two weeks ago.
The US authorities have accused Coke of being involved in illegal drugs and firearm trafficking and want him extradited to answer the charges.
Attorney-at-law Clyde Williams supports the stance being taken by the Government. "I think what must happen is that the provisions of the extradition law must take effect," Williams told The Gleaner. "I cannot see how the prime minister's commenting on the issue will impact on the situation."
He added: "What I will say is that the Government of Jamaica must act expeditiously in this matter."
However, University of Miami professor and attorney-at-law David Rowe believes the prime minister must speak.
"Under the doctrine of collective Cabinet responsibility, the Cabinet is the chief executive authority of the jurisdiction; the prime minister the ultimate authority for the executive action under an extradition treaty.
"The treaty uses the expression 'executive authority' in several articles. The prime minister acting through 'diplomatic channels' is responsible for treaty compliance," Rowe argued.