The semi-official Anatolia news agency said on Monday that police surrounded a supermarket after a tip-off that three suspects were inside, touching off a clash in which one policeman was injured.
The three managed to flee but were cornered several hours later when a new clash killed one suspect and left a second policeman injured.
A second suspect was captured and the third escaped, the agency said.
The report identified the victim only as a "terrorist", the term officials use to refer to rebels from the main Kurdistan Workers' Party (PKK) or leftist extremists, although Kurdish rebels are not generally active in the northeast of the country.
The PKK, which is blacklisted as a terrorist group by both the United States and the European Union, operates mainly in the Kurdish majority southeast Anatolia region where it launched a bloody armed campaign for autonomy in 1984.
The group has stepped up violence in recent months after calling off a unilateral truce declared in June 2004 on the grounds that Ankara's steps to expand Kurdish freedoms were insufficient.