Brown was one of five Senate Republicans who voted against a Republican House plan to privatize Medicare, saying he would fight waste and fraud to secure money for Medicare and Social Security.
"We are wasting tens of billions of dollars every month on duplicative programs in various areas of the budget, overpayments, defense and IT programs that are way over budget, and outright fraud," he said in a written statement to the AARP Bulletin.
Brown said he would like to repeal the Affordable Care Act, which he said cut billions from Medicare.
"First, we need to commit to current seniors and those close to retirement that they will absolutely continue to receive the benefits they have spent their entire careers working for, and are depending on," Brown said.
Warren (D) said she is opposed to privatizing or making unnecessary cuts to Medicare or Social Security, saying it would be a "breach of trust" to do so.
"At a time when big corporations are paying nothing in taxes, and hedge fund managers and oil companies are getting special tax breaks, we should not be asking seniors to live on less or talking about dismantling the system," Warren said in a written statement to the Bulletin.
"Instead, we need to cut health care costs across the board and do so in a way that improves quality."
She defended the Affordable Care Act, saying it streamlines the health care system and provides money for research for better health outcomes.