BOSTON — Defense attorneys across Massachusetts are reviewing their drunken driving cases and many prosecutors are suspending use of alcohol breath-test evidence while the state reviews possibly miscalibrated breath-analysis machines used by police.

The Massachusetts Bar Association is also calling for an independent review into the reliability of the tests, which the state says involve a “small number” of readings, but which the lawyer’s group and individual attorneys say could be much more widespread.

“It could be thousands,” said J. Albert Johnson, a defense attorney and longtime critic of breath-test evidence. “These people could seek dismissal or a new trial and certainly are entitled to release from incarceration.”

Johnson said lawyers at his firm are combing through their OUI cases to see if any clients are affected.

Meanwhile, district attorneys across the state are either not using breath-test evidence or seeking continuances of drunken-driving cases until the problem is resolved.

Suffolk District Attorney Daniel Conley, whose jurisdiction includes Boston and several suburbs, said in a statement that breath machines used in two Suffolk prosecutions “gave readings during calibration tests that were within the manufacturer’s guidelines but outside the narrower range imposed by the Code of Massachusetts Regulations.”

The Middlesex, Essex, Norfolk, Worcester, Northwestern and Cape and Islands district attorneys are among those also handing OUI cases differently pending the outcome of a review by the state Executive Office of Public Safety and Security.

That could be complete as soon as next week, agency spokesman Felix Brown said. He said a “small number” of readings did not comply with Massachusetts breath-test regulations.

The breath-analysis machine involved is called the Draeger 9510 and is used by state police and all local departments, Brown said.

“The Draeger machine has been shown to require calibration more often than other machines,” said Johnson, the defense attorney.

Company representatives did not respond to calls and email messages.

Martin W. Healy, general counsel for the Massachusetts Bar Association, wants the state attorney general to take over and appoint an independent investigator.

“In order for complete transparency it’s better to have someone not connected to defense lawyers or the prosecutorial community to take a look at these issues,” he said.

He likened it to the Annie Dookhan case, in which the former state lab worker was convicted of manipulating drug tests that affected thousands of prosecutions, although he also pointed out that Dookhan acted deliberately and there is no evidence of that in the breath-test case.

Nevertheless, the integrity of the legal system is at stake, he said.

“We’re just trying to ensure that people’s constitutional rights are being protected,” he said. “I think that’s a simple request.”

While not addressing the call for an independent investigator directly, a spokeswoman said Attorney General Maura Healey was aware of the situation and working with all parties.

“Any time there is a question about the validity of evidence used in a criminal proceeding, the attorney general is concerned,” spokeswoman Cyndi Roy Gonzalez said.

The situation is also being monitored at the Statehouse.

Sen. William Brownsberger, D-Belmont, chairman of the Senate Judiciary Committee, said his panel would seek more information before deciding if the Legislature should weigh in.