WASHINGTON — A top aide to Hillary Clinton at the State Department agreed to try to obtain a special diplomatic passport for an adviser to former President Bill Clinton in 2009, according to emails released Thursday, raising new questions about whether people tied to the Clinton Foundation received special access at the department.

The request by the adviser, Douglas J. Band, who started one arm of the Clintons’ charitable foundation, was unusual, and the State Department never issued the passport. Only department employees and others with diplomatic status are eligible for the special passports, which help envoys facilitate travel, officials said.

Mrs. Clinton’s presidential campaign said that there was nothing untoward about the request and that it related to an emergency trip that Mr. Clinton took to North Korea in 2009 to negotiate the release of two American journalists. Mrs. Clinton has long denied that donors had any special influence at the State Department.

The exchange about the passport, between Mr. Band and Huma Abedin, who was then a top State Department aide to Mrs. Clinton, was included in a set of more than 500 pages of emails made public by Judicial Watch, a conservative legal group that sued for their release.