WASHINGTON — Attorney General Eric H. Holder Jr., under fire over investigative tactics in leak cases, has opened internal discussions over tightening rules on when prosecutors may seek phone logs and other information that could identify reporters’ sources as he began a series of a meetings on Thursday with leaders of news media organizations.

According to an adviser familiar with the deliberations, Mr. Holder has discussed expanding a requirement for high-level review of proposed subpoenas for reporters’ phone records so that it would include e-mails. He is also examining whether to tighten a standard for when officials may seek such records without giving prior notice to the news organization.

President Obama has given Mr. Holder until July 12 to make his proposals, and Mr. Holder wants to complete an overhaul of department regulations on leak investigations before his tenure is over, said the adviser, who spoke on condition of anonymity because the deliberations are preliminary. Mr. Holder has given no indication that he intends to step down any time soon, however.

The Thursday meeting was intended to seek additional ideas and lay the groundwork for an internal push if prosecutors and intelligence officials balk at giving up some powers in leak investigations, the adviser said. Further meetings with both news organizations and government officials are planned, including another news media session on Friday.