"I found the leader that will help us deliver a safe society and a prosperous society, a really prosperous society, for all Americans", Trump said in introducing Pence.
"By picking Mike Pence as his running mate, Donald Trump has doubled down on some of his most disturbing beliefs by choosing an incredibly divisive and unpopular running mate", said John Podesta, Clinton's campaign chairman. "I didn't ask him to do it, but I don't think he should do it because it's different for him", explained Trump.
The full "60 Minutes" interview will air Sunday night at 7 p.m. ET.
A tiny piece of evidence that it can might have emerged Saturday morning, as Donald Trump held a press conference to unveil his presumptive veep, Indiana Governor Mike Pence.
"I accept your invitation to run and serve as vice president of the United States of America", Pence said.
During Trump's official introduction of Indiana Gov. Mike Pence as his running mate, the campaign adorned a fundraising email with a simple "TRUMP" atop a "PENCE", ditching an American flag-inspired interlocking T and P logo that attracted the attention of Trump critics and supporters alike.
Priebus says Trump is calling for a temporary ban on immigration from countries that harbor and train terrorists until the USA has a better vetting system.
Trump touted Pence as "outstanding in every way."
Following speculation that Trump's children had pushed their father to pick Pence, he insisted the governor was his "first choice". In the meantime, Trump heard last-minute pleas from backers of the other two vice presidential finalists, New Jersey Gov. Chris Christie and former House speaker Newt Gingrich.
Some 28 minutes in, Mr Trump said he was going to talk about Mr Pence.
When he did get round to talking about the man he hopes will boost his popularity among wavering Republicans, Mr Trump resorted to his notes, praising Mr Pence's track record as a congressman and governor of IN and describing him as a "solid, solid person".
Trump and Pence vowed to lead America, cut taxes, support small business and defeat the Islamic State terror group.
The US presidential hopeful explained his choice by praising the governor's fiscally conservative policies and his election in Indiana's Republican primary, which defied predictions from the party establishment.
He also revealed that he got the call to be Trump's running mate on Wednesday, even though on Thursday Trump told Fox News that he had yet to make a "final, final choice".
On finishing, Pence was embraced by members of his family, shook hands again with Trump and was kissed by the tycoon's daughters before the two candidates stood, rather stiffly, side-by-side.