WASHINGTON—The Justice Department has notified immigration judges that it will begin evaluating their job performance based on how quickly they close cases, aiming to speed deportation decisions and reduce a lengthy backlog.

The new quotas for judges to meet—laid out in a memo sent Friday to immigration judges—follow other directives by the department to expedite handling of cases. Attorney General Jeff Sessions has said that the backlog at the immigration courts allows people who should be deported to linger inside the U.S.

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