Lopez said: "In these difficult and trying times, I wish to express to the family of the deceased policeman our affection and that of the majority of Basque society which no longer tolerates the murderous and dastardly Eta."
Deputies observed a minute's silence in the parliament.
If confirmed, it would be the first deadly attack by Eta since December and its first action since regional elections on March 1 ousted a moderate nationalist Basque government in favour of the Socialists.
Arrogorriaga municipal authorities called a protest gathering against the attack for later in the day while Lopez called for a mass demonstration for Saturday evening in Bilbao.
Lopez said protestors should "utter a new cry from the Basque Country against Eta and in favour of peace and freedom".
"We are going to finish with them by applying all the force of the rule of law. They have shown us the way of grief, we will show them the way to prison," he said.
Unlike his predecessor, Juan Jose Ibarretxe of the Basque Nationalist Party, Lopez rejects any negotiations with Eta, who are blamed for the deaths of 825 people in its 40-year campaign to carve a Basque homeland out of northern Spain and southwestern France.