He added, 'In the coming months, I hope to visit with many of you and have a conversation about restoring the promise of America.'
Kristy Campbell, a spokeswoman for Bush, said he has not yet made a final decision on whether to seek the Republican Party's presidential nomination in 2016.
She said that he will announce his decision next year 'after gauging support' for a run.
'This is a natural next step and represents a new phase of his consideration process,' Campbell said.
That phase will include an expansion of Bush's political operations.
He said Tuesday he will start his own leadership political action committee in January, which will allow him to raise money and use it to support candidates in other races.
In his statement, Bush said the committee 'will help me facilitate conversations with citizens across America to discuss the most critical challenges facing our exceptional nation.
The PAC's purpose will be to support leaders, ideas and policies that will expand opportunity and prosperity for all Americans.'
The Democratic National Committee fired back in mere minutes.
'Isn’t this what he’s been doing all along?' asked DNC Communications Director Mo Elleithee. 'I don’t know what the difference is between "thinking about" running and "actively exploring" running, but I suspect it has a lot to do with keeping his name in the news.'
'However you see it, there’s no parsing this simple fact: Jeb Bush has fully embraced the failed economic agenda that benefits only a select few at the expense of the middle class. That’s not going to change no matter how many different ways he says he may run.'
Bush's announcement is also sure to reverberate throughout Republican politics and begin to help sort out a field that includes more than a dozen potential candidates, none of whom have formally announced plans to mount a campaign.
Should he ultimately decide to run, Bush can tap into his family's vast political network and his campaign would attract strong support from the same donor pool that other establishment-minded Republicans – New Jersey Gov. Chris Christie among them – need to fuel their own prospective campaigns.