The government exerted military force on villages left and right where fugitives were suspected of hiding.
この場合、次のような言い方ができますよ。
ーThe government exerted military force on villages left and right where fugitives were suspected of hiding.
「政府は逃亡者が隠れていそうな村々に手当たり次第軍事力を行使した」
to exert military force「軍事力を行使する」
left and right「手当たり次第」
fugitive「逃亡者」
ご参考まで!