Throwing his hat in the ring ... former Florida Governor Jeb Bush announced he’s planning to ‘actively explore’ a run for president. Picture: AFP Source: AFP

In a message posted on Bush’s Facebook page and Twitter account, the son and brother of past Republican presidents said he discussed the “future of our nation” and a potential bid for the White House with members of his family over the Thanksgiving holiday.

“As a result of these conversations and thoughtful consideration of the kind of strong leadership I think America needs, I have decided to actively explore the possibility of running for president of the United States,” the 61-year-old wrote. “In the coming months, I hope to visit with many of you and have a conversation about restoring the promise of America.”

However his announcement is likely to frustrate his mother and Bush matriarch, Barbara Bush, who last year said her son George W Bush should be the last in the family line of presidents.

“There are other people out there that are very qualified and we’ve had enough Bushes,” she told the Today show in the US in April 2013. “It’s a great country. There are a lot of great families and it’s not just four families.”

Dynasty ... former US President George HW Bush and wife, former First Lady Barbara, at the White House in May 2012. Picture: AP Source: AP

Kristy Campbell, a spokeswoman for Jeb 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 on 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.”

Brotherly love ... former Florida Governor Jeb Bush, left, clowns with his older brother, former US President George W Bush, at Orlando International Airport in Florida. Picture: AP Source: News Limited

Bush’s announcement is 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 Governor Chris Christie among them — need to fuel their own prospective campaigns.

A Bush candidacy also has the potential to affect the plans of Florida Senator Marco Rubio, who came up through Florida politics as a strong Bush supporter and is considering whether to seek re-election to the Senate or run for president in 2016.

A Bush candidacy also has the potential to affect Florida Senator Marco Rubio’s plans. Picture: AP Source: AP

New Jersey Governor Chris Christie is in the race for the 2016 GOP presidential nomination. Picture: AP Source: AP

Bush may also find competition from property tycoon and staunch Republican, Donald Trump, who said he’s likely to run in 2016.

“I can tell you there’s a very substantial chance I will (run),” The Apprentice star told MailOnline.

When asked whether the chances were better than 50-50, he said: “I don’t want to put a number on it.”

The 68-year-old is lining up support in primary states and publicly criticising potential rivals.

Could run ... Donald Trump said ‘there’s a very substantial chance’ he’ll run for President in 2016. Picture: Getty Images Source: Getty Images

Tuesday’s statement is the latest and most definitive signal that Bush plans to try and become the third member of his family to serve as president. In a TV interview this past weekend, he said he “would be a good president,” disclosed that he was writing an e-book about his time as governor that would come out in the spring, and promised to release about 250,000 emails from his time in office.

During his two terms as Florida governor, Bush pushed for large tax cuts, overhauled Florida’s education system and led the charge to eliminate race-based policies in college admissions and state spending.

Potential contenders ... Democrat Hillary Clinton and Republican Jeb Bush could go head to head in the 2016 presidential race. Picture: Supplied Source: Supplied

Since leaving office, Bush has continued to advocate for more changes to the nation’s schools, including the adoption of new education standards known as Common Core.

Those standards have drawn the ire of conservatives who view them as a federal intrusion into local classrooms, but Bush has continued to call them critical to overhauling the country’s education system, while seeking common ground with opponents by saying states should be allowed to develop their own education programs.

On the other side of the political fence, Hillary Rodham Clinton is reportedly mulling over when to formally announce her bid to seek the Democrat Party’s presidential nomination in 2016.

The former Secretary of State campaigned to become president in 2008, but lost to Barack Obama.