North Charleston, South Carolina (CNN) George W. Bush told voters here Monday that "we do not need someone in the Oval Office who mirrors and inflames our frustration" -- a clear swipe at Donald Trump during a campaign rally for his brother, Jeb Bush .

In his most political speech since he left office in 2009, George W. Bush said voters should choose a candidate who is "measured and thoughtful" over the loudest and angriest man in the room.

"I understand that Americans are angry and frustrated but we do not need someone in the Oval Office who mirrors and inflames our anger and frustration," Bush said. "We need someone that can fix the problems that cause our anger and frustration, and that's Jeb Bush."

Bush called the 2016 campaign a "serious election for a serious job," in a 20-minute speech that was both sober and at times light-hearted.

"I'm proud of his candidacy," Bush said about his brother. "I came here for two reasons -- one, because I care deeply about Jeb, and two, because I care deeply about our country."

Trump, for his part, said again Monday that the American people were not safe under President George W. Bush.

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"Excuse me, the World Trade Center came down during the reign of George Bush, right? I mean, it came down," Trump told reporters during a press conference in South Carolina. "We weren't safe. That was the greatest attack in the history of the United States." Trump also criticized Bush over the war in Iraq, which he said destabilized the Middle East.

George W. Bush did not take on those accusations head on, but he had a clear warning for his party about Trump. The former president pointed to the abundant "name-calling" in the 2016 election -- an apparent reference to the punches thrown between Jeb Bush and Trump in recent months -- and joked that according to their father, George H.W. Bush, "labels are for soup cans."

"(The) presidency is a serious job that requires sound judgment and good ideas," Bush said.

Although the former president did not once mention Trump's name in his remarks, the implicit message was clear: Trump is not a serious candidate.

"Strength is not empty rhetoric, it is not bluster," Bush said, but rather based on"integrity and character."

"In my experience, the strongest person usually isn't the loudest in the room," he added.

In a speech that was largely centered around national security and terrorism, Bush reflected on the attacks of September 11, 2001 -- and the "tough calls" he had to make in the days that followed — as he presented his brother as the most "measured and thoughtful" candidate in the GOP pack.

"When Americans woke up on September 11, we did not know that the world was forever changed that day," Bush said.

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He urged voters here to "look for a candidate who has genuine respect for the United States military (and) who will support them on the battlefield and when they return home."

The long-running tensions between Jeb Bush and Trump boiled over on Saturday at the Republican debate in Greenville , when Trump attacked George W. Bush's national security record. The New York real estate mogul called the former president's decision to go to war in Iraq a "big fat mistake."

Jeb Bush hit back with force.

"My dad is the greatest man alive, in my mind. While Donald Trump was building a reality TV show, my brother was building a security apparatus to keep us safe and I'm proud of what he did," he said.

Trump took things one step further, saying it was under George W. Bush's watch that the World Trade Centers in Manhattan fell on 9/11.

"That's not keeping us safe," the New Yorker said, as the audience booed loudly in disapproval.

Photos: 9/11 tributes across the nation Photos: 9/11 tributes across the nation The sun rises over Lower Manhattan and One World Trade Center, at left, on Friday, September 11, in a view from Jersey City, New Jersey. The nation is marking the 14th anniversary of 9/11, the deadliest terrorist attack on U.S. soil. Nearly 3,000 people died that day. See other images of 9/11 events: Hide Caption 1 of 16 Photos: 9/11 tributes across the nation Gary Mascitis, 14, pays tribute to his uncle during an anniversary ceremony for the attacks in New York. Two hijacked planes hit the World Trade Center on 9/11. A third plane crashed into the Pentagon outside Washington and a fourth into a Pennsylvania field. Hide Caption 2 of 16 Photos: 9/11 tributes across the nation American flags are lowered to half-staff at the Washington Monument on September 11. Hide Caption 3 of 16 Photos: 9/11 tributes across the nation Honor guards salute during the national anthem in a 9/11 ceremony Friday at Indianapolis International Airport. Hide Caption 4 of 16 Photos: 9/11 tributes across the nation Law enforcement officials stand at attention Friday during the national anthem in an anniversary ceremony in New York in commemoration of the 9/11 attacks. Hide Caption 5 of 16 Photos: 9/11 tributes across the nation Engine Company 205/Ladder Company 118 in New York's Brooklyn Heights remember the eight firefighters it lost on 9/11, including six who died in their firetruck under the rubble. Hide Caption 6 of 16 Photos: 9/11 tributes across the nation President Barack Obama and first lady Michelle Obama lead a moment of silence on the White House South Lawn at 8:46 a.m. Friday -- the time when the first hijacked plane hit the World Trade Center on 9/11. Hide Caption 7 of 16 Photos: 9/11 tributes across the nation A bugler plays taps during Friday's ceremony on the South Lawn of the White House. Hide Caption 8 of 16 Photos: 9/11 tributes across the nation Roses are placed Friday at the National September 11 Memorial in New York before a ceremony commemorating the 14th anniversary of the attacks. Hide Caption 9 of 16 Photos: 9/11 tributes across the nation Terry Miller, right, and Chris Miller, center, look for the name of their brother Robert Cromwell Miller at the Empty Sky memorial to New Jersey's victims of 9/11. The memorial is in Jersey City across the Hudson River from the World Trade Center site. Nephew James Miller, left, joins them Friday. Hide Caption 10 of 16 Photos: 9/11 tributes across the nation Yachiyo Kuge carries a lantern to place at the Wall of Names at the Flight 93 National Memorial in Shanksville, Pennsylvania, on Thursday, September 10. Kuge is the mother of Toshiya Kuge, a Japanese passenger who died on United Airlines Flight 93 on 9/11. The plane crashed in Pennsylvania as passengers and crew tried to overcome the hijackers. Hide Caption 11 of 16 Photos: 9/11 tributes across the nation Some 3,000 flags erected by Pepperdine University students and staff honor the victims of 9/11 on the Malibu, California, on September 10. Hide Caption 12 of 16 Photos: 9/11 tributes across the nation A visitor tours the crash site at the Flight 93 National Memorial on September 10. The visitor center complex was dedicated in honor of the victims of Flight 93 on the evening of the 14th anniversary of the 9/11 attacks. Hide Caption 13 of 16 Photos: 9/11 tributes across the nation A visitor views a display at the Flight 93 National Memorial visitor center on September 10. Hide Caption 14 of 16 Photos: 9/11 tributes across the nation Flags carry the names of the 9/11 victims at Memorial Park in Omaha, Nebraska, on September 10. Hide Caption 15 of 16 Photos: 9/11 tributes across the nation The Tribute in Light illuminates the sky behind One World Trade Center and the Lower Manhattan skyline on Wednesday, September 9. Hide Caption 16 of 16

Since leaving Washington in 2009 after eight years in the White House, Bush has not shown interest in being in the public spotlight or playing a leadership role within the Republican Party. His visit to North Charleston comes as other members of the Bush clan have also started to play a more active role in Jeb Bush's presidential campaign. In New Hampshire, Bush's mother and former first lady, Barbara Bush , campaigned with her younger son.

On Monday, George W. Bush also discussed life after the White House, which he lightheartedly referred to as "the after life."

"Laura and I loved our years in Washington, but we really don't miss it too much," he said, bringing the audience to laughter.

He joked that the couple now spends a lot of time on their ranch in Texas, and that that as tree farmers, he still gets opportunities to practice his "stump speech."

He also quipped about his new hobby of painting: "Let me assure you, I know that the signature's worth more than the painting."

There were plenty of attendees at the North Charleston Coliseum who said their main motivation for coming to Jeb Bush's rally Monday night was to see an ex-president in person.

Sharon Hickey, a New Hampshire resident who rents a home in South Carolina for a part of the year, said it was "wonderful" to see George W. Bush campaign for his brother.

"We're honored to be here to see, to be in the presence of, a former President," Hickey said.

Joe Kelley, a retired fighter fighter from Boston who owns a second home in Murrells Inlet, is currently undecided but leaning towards Jeb Bush and Marco Rubio. As he waited to George W. Bush to take the stage, he said he thought the ex-President did a "fine enough job" in the White House.