In the second debate, fireworks between Michelle Wu and Annissa Essaibi George

Boston mayoral candidates Annissa Essaibi George (left) and Michelle Wu.

The fireworks came from the start of Tuesday’s debate, as Boston’s two mayoral candidates attacked and parried in their most spirited encounter so far in the campaign.

Their face-off began with City Councilor Annissa Essaibi George, the underdog, going hard at front-runner Michelle Wu over what Essaibi George claims is Wu’s “inconsistent” messaging on admissions to the city’s three prestigious exam schools.

Recent reforms should increase the diversity of students admitted to those schools, but reaction to the changes varies widely across the city, with particular ire coming from more affluent white communities such as West Roxbury, where Essaibi George did well in the preliminary election.

“Talk to me please about why you are delivering a different message depending on which community you’re in,” Essaibi George demanded.

“That’s simply not true,” Wu countered, before giving a lengthy response that the exam school process should be equitable, fair, and reflective of the diversity in the city.

Essaibi George shot back: “She didn’t answer my question. I’d like to know why you have been inconsistent, neighborhood by neighborhood,” she insisted.

And so it went during the second formal debate between the two candidates, with Essaibi George repeatedly prodding and admonishing Wu — for taking credit for Essaibi George’s push to hire more mental health clinicians; for a free MBTA plan that Essaibi George said is too costly; and for a rent stabilization vision that Essaibi George said is detrimental to longtime mom and pop landlords.

Wu, who was mostly on the defense, swatted away her rival’s criticisms, but at one point she urged peace.

“The city of Boston deserves better,” she said, looking at Essaibi George and then to the camera. “Our country and our democracy barely survived four years of Trump, and the types of campaigning that involve negative attacks, personal attacks, falsehoods, and fear mongering. This is not what I wanted this mayoral race to turn into.”

With the election ending in less than two weeks and Essaibi George trailing Wu by 32 percentage points in a poll released Tuesday morning, the Dorchester councilor needed to show that the race is not over and that she can chip away at her rival’s lead.

Wu’s mission was to do no harm and stay above the fray, according to political observers, and avoid any land mines Essaibi George threw her way. But it was not easy.

When Essaibi George attempted to chide Wu for taking credit for the push for more clinicians, Wu gently reminded her that work began long before Essaibi George joined the council.

“I was proud to support the work that happened on the council in pushing for the number of clinicians to go from two to 19, and also to have been around before you joined the council, when then-councilor Ayanna Pressley led the charge on this,” Wu said.

For the most part, the two candidates’ approaches fell largely in line with what many in political circles had anticipated the night would bring: Essaibi George was scrappy, Wu optimistic.

The debate was a contrast in style and substance, as the candidates tangled over police reform, education access, and public transportation.

The candidates did agree on the need to act quickly on climate issues and on quality of life issues, such as fixing pot holes, as well as the importance of providing better constituent services. They both offered a vision for boosting beleaguered Madison Park Technical Vocational High School. They each supported Acting Mayor Kim Janey’s new plans to address the myriad crises at Massachusetts Avenue and Melnea Cass Boulevard, including declaring addiction and homelessness a public health crisis.

Early on, Essaibi George took aim at one of Wu’s signature policy proposals: making the T free, saying such a move would require cooperation from Beacon Hill, and questioned how the city would make up for the lost fare revenue.

“It is unfair to ask the people of Boston to pay that price tag,” Essaibi George said.

Wu did not directly address the funding question, but struck an aspirational tone, casting herself as an optimist whose ambitions match the city’s needs.

“I’m not running for mayor to say what we can’t do,” Wu said. “I’m fighting for what we need and deserve.”

At one point, both women seemed to struggle when asked about their household incomes. Wu hesitated when asked whether her family’s household income of just over $200,000 placed it in Boston’s “upper class.”

“Upper middle class,” she said after a pause.

Wu has released joint tax returns showing her household income.

Essaibi George said her family has a “pretty high income” and does sit in Boston’s “upper class.”

Essaibi George, who said her income was over $100,000, said she has released her income tax returns to the media. But she has not released the tax returns of her husband, a real estate developer. Her campaign has declined to answer a number of questions about his businesses.

Essaibi George also asked Wu to explain her ties to campaign donor Terry Considine, a Republican businessman and the father of Elizabeth Likovich, one of Wu’s closest friends and godmother to her older son.

“You’re before the people of Boston asking to be their mayor,” Essaibi George said. “You should be clear. You should be more transparent.”

Records reviewed by the Globe show that Wu and her husband purchased a two-family home in Roslindale with Likovich, her college friend, and Likovich’s husband. After 14 months, the other couple sold their portion of the home to Wu and her husband. The records show that Wu and her husband paid fair market value.

The Globe examined the connections between Wu and the family — suggestions of impropriety have long been quietly pushed in political circles — and found no evidence of inappropriate activity by Wu.

Essaibi George raised the connection when asked about the business practices of her husband, Douglas R. George, who the Globe reported Sunday owns some 55 properties in Boston with an assessed value of $54 million. Essaibi George’s husband has a history of late tax payments and code violations, and has clashed with city inspectors.

“There’s absolutely no wrongdoing that happened here,” Wu told Essaibi George in response to repeated inquiries about her connections to Likovich’s family. “There’s simply nothing here and I’m disappointed to see the tactics that are being used.”

Essaibi George also said that Wu’s husband, Conor Pewarski, has served as the “resident agent” for a limited liability company that owns a three-family home outside Harvard Square in Cambridge. Wu’s college roommate and her relatives set up the company, which has owned the property since 2004. It is a common arrangement; Essaibi George’s husband has more than a dozen such companies.

Massachusetts requires that all limited liability companies have a “resident agent,” who serves as a legal contact and not an owner or manager.

Records show that Pewarski became the company’s resident agent in 2013 when the previous one moved to Colorado, where Wu’s college roommate is from. The most current records at the secretary of state’s office list Pewarski’s previous address in the South End, where he and Wu have not lived since 2015.

Andrew Ryan of the Globe staff contributed to this report.