Lawmakers are poised to enact a bill strengthening Massachusetts’ much-maligned public records law, seen as among the weakest in the country.

The legislation unveiled Monday, a House-Senate compromise, would allow judges to make the state, cities, and towns pay lawyers’ fees if a court found they inappropriately withheld public records.

Advocates say that provision would encourage government officials to fulfill public records requests by creating consequences for failing to comply with the law. And they praised the whole package as a huge leap forward.

“This bill will add considerable freedom of information to Massachusetts and make for more openness and accountability in government,’’ said Pam Wilmot, executive director of Common Cause Massachusetts. “It’s a very strong bill. It moves us from near the back of the pack in the nation to somewhere certainly in the top half.’’

But the state’s top lobbyist for cities and towns warned the bill could burden local officials with new costs and unrestrained litigation. Geoffrey C. Beckwith, executive director of the Massachusetts Municipal Association, said the provision that would allow the awarding of attorneys’ fees when a public record is found to be wrongly withheld could lead to “excessive and costly litigation’’ against communities working in good faith to fulfill requests.

The bill would also require digital as opposed to paper responses, and limit the sometimes exorbitant fees that municipalities and the state charge for providing public information. Beckwith worried that such limits could drain municipal coffers.

Under current law, state agencies and municipalities are supposed to respond to requests for public information — such as government e-mails and payroll records — in 10 days. But it can take weeks, months, or years for officials to actually produce the requested documents. The bill would give agencies and communities more time to initially respond to requests for public information, but would mandate stricter timelines for fulfilling such requests.

Many government records are currently presumed to be public unless protected by an exemption, such as those for active investigations and trade secrets. But the Legislature and judiciary are mostly exempt. The bill would not change that part of the law.

Gavi Wolfe, legislative counsel at the ACLU of Massachusetts, said the bill would modernize the law to make sure “in the digital age, information is provided efficiently, electronically to people who want information about the workings of their government.’’

Wolfe said the way the bill is structured regarding judges’ ability to award legal fees is a “terrific step forward for enforcement’’ because the legal language has a “presumption’’ in favor of the awarding of fees.

“We have been so far out of the mainstream — 47 other states and the federal government provide for attorneys’ fees — simply allowing for those fees is a real step forward in and of itself, and this bill goes beyond that,’’ he said.

But even as advocates lauded the compromise, its major provision falls short of what they had originally hoped for and the way the law works in some other states: a mandate, with only a few exceptions, that would require judges to award such fees in cases where the government was found to have wrongly withheld documents.

Thus, some praise for the legislation was tempered. Robert Ambrogi, a First Amendment attorney and executive director of the Massachusetts Newspaper Publishers Association, said the bill achieves a balance between competing interests but does not go as far as he would have liked to close exemptions, reduce fees, and penalize agencies that fail to comply.

The bill would extend how long agencies and municipalities have to respond to public records requests, from 10 calendar days to 10 business days — with the option for a five-business-day extension for state agencies and a 15-business-day-extension for cities and towns. Government officials could also ask the secretary of state’s office for a further extension of 20 business days for agencies or 30 business days for municipalities.

That provision could prompt worry from short-staffed towns and agencies that they will have to divert resources to meet the new deadlines.

The House will take up the bill on Wednesday, and the Senate soon thereafter. Should both chambers give final approval to the bill, it will go to Governor Charlie Baker. He appeared to telegraph concerns through a spokeswoman Monday.

The administration, said press secretary Lizzy Guyton, will carefully review the bill, “including timeframes required for responses, to ensure that agencies and municipalities are able to reasonably meet deadlines for voluminous requests.’’

Baker could sign the bill into law, let it become law without his signature, veto it, or send it back to the Legislature with recommended changes.

The legislation would also clarify that documents from the MBTA Retirement Board, which manages a $1.6 billion pension fund for transit workers, are public record. A Suffolk Superior Court judge already made a preliminary ruling that the fund’s documents are public after The Boston Globe sued the board for records on the taxpayer-funded pension. The board is continuing to fight that ruling.

Senate president Stanley C. Rosenberg praised the compromise as a whole, saying: “The bill increases transparency and improves access by increasing affordability and shortening turnaround time.’’

And Representative Peter V. Kocot, a Northampton Democrat who helped draft the measure, noted that “public records are paid for by taxpayers. And taxpayers should not face unnecessary burdens of time or cost to access information that is theirs.’’

Todd Wallack and Beth Healy of the Globe staff contributed to this report. Joshua Miller can be reached at joshua.miller@globe.com.