A group of conservative Republicans sent a criminal referral to the Justice Department Wednesday asking prosecutors to consider bringing charges against former FBI Director James Comey, former Attorney General Loretta Lynch, former Secretary of State Hillary Clinton and others involved in the probe into Mrs. Clinton’s emails.

They also complained that the FBI and Justice Department mishandled the so-called “Steele dossier” with salacious and unverified claims about then-candidate Donald Trump.

The 11 GOP lawmakers, led by Florida Rep. Ron DeSantis, said the taint of the two matters is so widespread that it demands investigations of Mr. Comey, Ms. Lynch, Mrs. Clinton, former FBI Deputy Director Andrew McCabe, former Deputy Attorney General Sally Yates, former acting Deputy Attorney General Dana Boenta, FBI Agent Peter Strzok and FBI lawyer Lisa Page. Those latter two were the FBI employees whose text messages revealed some of the sordid inner workings of the Clinton email probe.

“Because we believe that those in positions of high authority should be treated the same as every other American, we want to be sure that the potential violations of law outlined below are vetted appropriately,” the lawmakers said in a referral letter.

They said Mr. Comey should be investigated for allowing politics to influence his decision not the recommend charges against Mrs. Clinton for her email misuse, and for possibly leaking classified information in memos he indirectly fed to the press after he was fired last year.

Mrs. Clinton deserves investigation because her campaign and the Democratic National Committee didn’t disclose that they paid for the research that produced the salacious Steele dossier, the lawmakers said.

Ms. Lynch, they said, may have threatened reprisal against an FBI informant who raised questions about Mrs. Clinton’s activities as secretary.

Mr. McCabe was dinged for having been found to have lied to Mr. Comey and to both Justice Department and FBI investigators about his own leaks to the press.

Agent Strzok and Ms. Page, the two FBI employees whose text messages captivated Washington earlier this year, should be probed for their roles in the Clinton email investigation, the GOP congressmen said.

And then they asked for a catch-all probe into anyone at the FBI or Justice Department who approved surveillance on former Trump campaign aide Carter Page based in part on the Steele dossier.

The referral joins a request from Sens. Charles E. Grassley and Lindsey Graham, who earlier this year asked the Justice Department to investigate Christopher Steele, the former British spy and author of the Steele dossier.

Mr. Grassley, chairman of the Judiciary Committee, and Mr. Graham, chairman of a key subcommittee, said Mr. Steele misled the FBI by pushing the contents of his dossier, even though he has since said in a court case in London that he doesn’t have confidence in much of his reporting.

The lawmakers said that since the Justice Department has pursued Trump campaign figures on charges of lying to the FBI, it made sense to also look at Mr. Steele.