The Supreme Judicial Court has tentatively approved a new slate of rules for accessing Massachusetts court records, including partially restoring access to basic criminal court information online.

Under the new rules, the courts will gradually start allowing the general public to look up basic docket information online for almost all criminal cases — such as the status of the case and list of upcoming hearings — by entering the docket number for each case; users will not be able to look up criminal cases by defendant name online. The courts already allow the general public to look up basic information on most civil cases on the Internet.

The move comes a month after the courts abruptly blocked lawyers and journalists from accessing online data about criminal cases (except for cases where lawyers had entered an official court appearance), sparking an outcry from reporters, prosecutors, attorneys, and clerks. The courts said they made the move because they were concerned that certain organizations were systematically downloading civil case information (and could have potentially downloaded criminal data as well). But the courts declined to name the organizations downloading the data, provide more details about how they were misusing the information, or fully explain how it caused any harm.

In a statement, the courts said they tried to balance the need to give the public greater access to court records, while also trying to guard the privacy of litigants, victims, and witnesses.

They also said they tried to respect the Legislature’s intent to restrict access to the state’s centralized database of criminal records (known as CORI), even though the federal courts have ruled that the public has a constitutional right to access the indexes of court cases. Citizens will still be able to search for criminal cases by defendant name at the courthouse, but not online.

The new rules also cover a variety of other issues. For example, the rules make it clear that members of the public can use a mobile phone or other device to take a picture of a court document, instead of having to pay a clerk roughly $1 per page to make a copy.

In addition, the rules give the courts broad discretion to provide or deny statistics about court cases, but also direct the courts to generally deny requests for raw data — potentially making it harder for journalists and researchers to perform their own analysis of court records.

The courts indicated that a provision of the rules dealing with attorney access to cases was provisional and could be refined later. “We are looking for greater attorney access,’’ said Martin W. Healy, chief legal counsel for the Massachusetts Bar Association, who added that the group was generally pleased with the rules.

Robert Ambrogi, an attorney and executive director of the Massachusetts Newspaper Publishers Association, had a mixed reaction.

Ambrogi praised the SJC for making it easier to copy court records, but was disappointed the rules continue to severely limit the public’s access to actual documents online for now and bar people from searching for criminal cases by defendant name online.

“In this day and age, court records should be equally available to the public online and in person,’’ Ambrogi said.

Todd Wallack can be reached at twallack@globe.com. Follow him on Twitter @twallack.