But Tenet's board rejected that offer, and adopted a "poison pill" measure to fend off the bid.
Tenet's shares have recently been trading above $6. But the company said Monday it will review the revised offer and make a recommendation. It said shareholders should take no action for now.
Tenet shares fell 16 cents, or 2.4 percent, to $6.50 in pre-market trading while Community Health shares slid $4.25, or 13.3 percent, to $27.65.
Community Health Systems runs 130 hospitals in 29 states, and focuses on fast-growing and non-urban markets. Tenet runs 50 hospitals spread across 11 states, and most of its facilities are in urban and suburban communities.
Earlier this month, Tenet filed a lawsuit that alleges Community Health Systems bilked Medicare, artificially inflating the value of its shares. The Franklin, Tenn., company said the allegations in the lawsuit are "irresponsible and inaccurate."
Community Health Systems disclosed Friday that it has received a subpoena from the U.S. Department of Health and Human Services related to an investigation of potentially improper Medicare and Medicaid claims. It said the subpoena concerns emergency department processes and procedures, including a third-party software system, along with information about emergency department physicians, including financial details. It said it will cooperate fully with the investigation by the health department's office of the inspector general.
Community Health Systems said the state of Texas requested similar information in November.
The company said it received the subpoena on April 8. The company said it does not know if the subpoena is connected to any of the allegations in Tenet's lawsuit, which was filed April 11.
The company said it will address Tenet's lawsuit in a conference call on April 28. Community Health Systems will also discuss first-quarter results on that conference call.