The veteran Italian boss has named the Reading defender in a long-list of 29 for the upcoming World Cup qualifiers but has shown no remorse for his recent comments
Kelly was left out of February's friendly against Poland with the manager claiming that the former Ireland captain had threatened not to travel with the squad should he be dropped from the starting XI.
The Reading defender subsequently released a statement slamming the "untrue and unwarranted comments made by Giovanni Trapattoni".
Asked if he had apologised for what Kelly had called attempts to "defame" his commitment, the 73-year-old Italian told reporters: "Why? I don't need to apologise? Kelly is available, he's in the squad. After we decide who plays, tactically or depending on the opponent.
"It’s clear, he's in the squad. We clarify what we need in every game, offensive or not.
"For 30 years dealing with journalists in other countries I have been patient. I am also intelligent, I know what you want, what you wish or what you need [a soundbite]. It is my law to deal with this matter directly."
The former Italy manager was also asked about Darron Gibson's international future, with the Everton midfielder having once again turned down the opportunity to join up with the squad.
"I saw him, he played very well in the last game," he added.
"[Gibson] said: 'Thanks, but at the moment I don't wish to make a controversy, I am not ready. I will be available [in the future].
"What can I do, make him come with us, beat him?"
Keith Andrews, Greg Cunningham and Andy Keogh have also been left out of the squad. Bolton's Andrews is suffering with an achilles injury while Bristol City left back Cunningham's place is taken by the fit-again Marc Wilson of Stoke.
West Ham's Joey O'Brien makes a return after being overlooked for the Poland friendly. The list of 29 will be trimmed to 23 next week and the squad will get together on March 17.
Provisional Republic of Ireland squad to face Sweden and Austria:
Westwood, Forde, Randolph, O'Shea, St Ledger, Clark, Wilson, Coleman, Kelly, O'Dea, O'Brien, McShane, Pearce, Ward, Whelan, McCarthy, Green, Hendrick, McGeady, Pilkington, McClean, Brady, Keane, Long, Doyle, Sammon, Walters, Cox, Hoolahan