Warner was part of a string of high-powered Virginia Democrats who in early June pressed then-state senator Phillip P. Puckett not to go through with plans to give up his seat in the middle of a bitterly partisan battle over health care.

A Warner spokesman acknowledged Friday that the conversation occurred, but he emphasized that the senator had made no explicit job offer.

Puckett eventually resigned, throwing control of the chamber to the Republican Party and dooming Gov. Terry McAuliffe’s top legislative priority — expanding Medicaid under the Affordable Care Act. The incident also triggered a federal investigation into Puckett’s surprise exit, which came at a time when Republicans were planning to give Puckett a job on the state tobacco commission and confirm his daughter to assume a judgeship.

On June 6, three days before the state senator’s resignation became official, Warner called Puckett’s son, Joseph, and discussed an appointment to the federal bench as well as a potential corporate position for Martha Puckett Ketron, according to Joseph Puckett’s attorney, Charles E. “Chuck” James Jr. of Williams Mullen.