Mr Edafe said the duo were nabbed on Wednesday by Policemen attached to the Eagle-Net Patrol Team.
The police did not immediately confirm fatalities but said some construction workers who sustained gunshot wounds were stable at the hospital.
Attacks on the police have become rife in the southeastern state recently.
“All the policemen posted on duty on highways must be at alert and not use their duty posts as a means of extortion,” Mr Oyediran warned.
The cook slapped one of the policemen who arrested her for being in a ‘black spot’ late at night. She was given a bail of N500, 000 with two sureties each in like sum.
The victims were on motorcycles on their way to their farms when they were ambushed and killed.
Governor AbdulRahman AbdulRazaq of Kwara has donated dozens of bulletproof vests to Nigeria’s security forces as insecurity worsens across the country.
The police confirmed three separate attacks on personnel across the oil-rich state overnight.