ALBANY — In a strongly worded response to a New York State Board of Elections report alleging illegal fund-raising activities by a team of people with close ties to Mayor Bill de Blasio, a lawyer for several of the implicated parties has accused the board of “a shocking lack of understanding or a complete disregard of the most fundamental aspects of the state’s election laws.”

The letter, drafted by Laurence D. Laufer, a longtime campaign finance lawyer who also represents the mayor’s re-election campaign, came two days after accounts in the news media of a January report from Risa S. Sugarman, the board’s chief enforcement counsel. The report, which was confidential, found “willful and flagrant” violations of election law by a group of political operatives known as Team de Blasio, which was formed in 2014 to try to retake the State Senate for Democrats, who are in the minority in Albany’s upper chamber.

According to Ms. Sugarman’s account, Team de Blasio tried to evade contribution limits by channeling hundreds of thousands of dollars through county and state campaign committees, which then disbursed money to three ultimately unsuccessful Senate campaigns. Such committees can receive larger donations — up to $102,300 — than individual candidates, who are limited to $11,000 per donor during a general election for the State Senate.

The report was reviewed by the board’s four commissioners and forwarded to Cyrus R. Vance Jr., the Manhattan district attorney, prompting a criminal investigation that is being conducted with agents of the Federal Bureau of Investigation, who have been accompanying Mr. Vance’s investigators as they serve subpoenas and conduct interviews.