PITTSBURGH — West Penn Allegheny Health System has agreed to pay more than $1.5 million to settle claims it violated the law by offering doctors below-market rents so the physicians would refer patients to the network’s hospitals, federal prosecutors said Wednesday.

Allegheny Health Network, a Highmark-owned hospital network that includes the five West Penn Allegheny Health System hospitals, said the settlement resulted from a “self-audit and voluntary reporting” to federal officials.

U.S. Attorney David Hickton confirmed that in announcing the settlement. The allegedly illegal activity began in the mid-2000s, with most of it occurring between 2008 and 2012, federal prosecutors said.

That was before Pittsburgh-based health insurer Highmark bought the five-hospital West Penn network and created the Allegheny Health Network with two other hospitals it also acquired: Jefferson Regional Medical Center in the city’s South Hills suburbs and Saint Vincent Health System in Erie.

West Penn had experienced financial problems before the Highmark takeover and has since continued to lay off hundreds of workers to cut costs.

Allegheny Health Network remains locked in a financial battle with the much-larger University of Pittsburgh Medical Center, which has 20 hospitals. Highmark subscribers are allowed to use UPMC doctors and hospitals as in-network providers. When that deal expires next year, Highmark customers will have to pay more to continue using UPMC doctors and most of its hospitals.