D.C. Council member David Grosso is seen during a swearing-in ceremony at the Washington Convention Center on Wednesday. (Matt McClain/THE WASHINGTON POST)

Members of the D.C. Council tried Wednesday to move past the tumult of the past two years, with several using swearing-in ceremonies to highlight the need to rebuild public trust in the legislative body.

Six council members took their oaths of office at the Walter E. Washington Convention Center, marking the beginning of a new two-year term — the 20th since Congress granted the city limited self-government in 1975.

The previous term ranks among the council’s most dismal. Two members — Harry Thomas Jr. (D-Ward 5) and Chairman Kwame R. Brown (D) — resigned in 2012 shortly before pleading guilty to federal felony charges. The ongoing troubles created a raw atmosphere and frequently put members’ ambitions, frustrations and resentments on public display.

But Chairman Phil Mendelson (D-At Large) said Wednesday the new term is an opportunity to start fresh. “I do believe that our government is turning the corner,” he said. “Although there are unfinished investigations, this council has returned its focus to business.”

The District’s ethics board continues to probe the 2008 actions of Jim Graham (D-Ward 1) in the council’s handling of the city lottery contract, which is also the subject of a federal probe. Federal authorities continue to investigate Mayor Vincent C. Gray’s 2010 campaign. And elections officials have yet to close their inquiry into Brown’s 2008 council campaign.

The council’s business early on could include changes to the city’s campaign finance laws.

Gray (D) said after the ceremony that campaign finance reform is his foremost legislative priority for the new year. He last year forwarded to the council a bill drafted by Attorney General Irvin B. Nathan that would address “pay-to-play” concerns, in part by limiting campaign activities of lobbyists and city contractors, but it languished in the closing weeks of the council term.

“It’s something we hoped would be acted on,” Gray said. “It wasn’t and we really feel it ought to be moved expeditiously.”

But Mendelson said he was skeptical new laws alone could cure the city government’s ethical ills. He, along with several colleagues, resisted even modest restrictions on the potentially illicit use of money orders to hide the identities of campaign donors.

“To be sure, there are reforms we can and should enact,” he said. “But the solution to someone breaking the law is not to pass new one, rather it is to hold your elected representatives accountable. ”

The council’s newest member, David Grosso (I-At Large), was more overt, calling on his colleagues to “establish an ethical framework” in order to create a council that is “above reproach.”

Residents, he said, “believe we can do a lot better.”

“They think it is important for council members to remember voters more than contributors,” Grosso continued.

Muriel Bowser (D-Ward 4), who is starting her second full term, said the council had in some cases “failed to lead with urgency” to solve the city’s problems, leading to a disenchanted electorate.

“We can’t pretend today that we haven’t let our people down, in some big ways, in some obvious ways,” she said.

Beside Bowser and Grosso, Yvette M. Alexander (D-Ward 7), Marion Barry (D-Ward 8), Jack Evans (D-Ward 2) and Vincent B. Orange (D-At Large) were sworn in to new terms Wednesday. Mendelson was sworn in last month after winning a special election for the chairmanship, replacing Brown.

In a short meeting Wednesday afternoon, the council approved rules for its new term. In one small but significant change, the new rules require members and staff to use their official e-mail accounts to conduct public business no later than March 1.

The D.C. Open Government Coalition sued the council in October after it refused to share work-related e-mails sent by members on their personal accounts. The e-mails, the council said, were not in its possession and hence not subject to public records laws. The new policy will help ensure that official e-mails remain in the council’s possession.