Speaking to BBC Scotland’s The Nine on Wednesday, Mr Jack said he had an agreement with leader of the Scottish Conservatives, Douglas Ross, that they would “not declare” their hand throughout the vote to replace Boris Johnson.
“At the end of it, the Scottish conservatives would 100% back, whoever was prime minister, and we agreed not to declare our hand, either before, during or after, and to get right behind the Prime Minister and that’s where we are and I’m very pleased that we’re in that position.”
Mr Jack said he did not reveal to Ms Truss who he backed in the election.
He was also asked about details of the new energy package to freeze utility bills that will be announced on Thursday.
Ms Truss is expected to announce plans to cap household energy bills at £2,500 per year.
“It is a very good package for domestic users and for business users of electricity,” Mr Jack said.
“I’m absolutely delighted with it. It’s a package that’s reflected for instance, if you think back to furlough, it will deliver for the whole of the United Kingdom.”
But Mr Jack would not reveal any details on levels of spending or borrowing.
He added: “I can only say we’ll have to wait until Thursday for the detail because that’s what we’ve agreed rightly with the Speaker. But I think people will be very pleased with it.”
The Dumfries and Galloway MP urged the Scottish Government to “come with” the UK government on nuclear power.
Mr Jack ruled out any changes to UK law which would allow a second referendum.
He said: “We’re not having a referendum. The First Minister has taken her case to the Supreme Court. They will deliberate sometime between October 11 and the end of the year, I suspect.
“We don’t see any need to make any adjustments around the rules of referenda at all, because as I say we’re focused on delivering for people, not having constitutional upheaval through a referendum campaign.”