Kindred Healthcare Inc., a provider of long-term medical care, made an unsolicited offer to buy rival Gentiva Health Services Inc. for about $533 million in a cash-and-stock deal.

Gentiva turned down the $14-a-share offer on May 13, as well as a bid last month of $13 a share, according to correspondence between the two companies published by Louisville, Kentucky-based Kindred today. Kindred valued the transaction at $1.6 billion including assumed debt.

“It’s a mistake for the board not to enter negotiations,” Sheryl Skolnick, an analyst with CRT Capital Group LLC, said in a telephone interview from Stamford, Connecticut. “Kindred is the logical strategic buyer. It really needs to be a strategic buyer with the level of debt Gentiva has.”

About $118 billion of health-care mergers and acquisitions were announced or proposed last month, a record, according to data compiled by Bloomberg that dates back to 2002. It’s almost as much as the $174 billion that was earmarked for health-care deals for all of last year, the data show.

Kindred offered to pay $7 a share in cash and $7 a share in stock, and is willing to pay the total amount in cash, the company said in a statement today. The $14-a-share bid values Atlanta-based Gentiva at 64 percent more than its closing share price yesterday of $8.54.

“Our board continues to believe that our long-term strategy as a stand-alone company will generate substantially more value to our shareholders,” Gentiva Chairman Rod Windley wrote in the May 13 letter to Paul Diaz, Kindred’s chief executive officer.

The combined company would have annual revenue of about $7.2 billion, serve 127,000 patients per day, operate in 47 states and employ about 110,000 people, Kindred said. The deal would fuse two “highly complementary businesses” by joining Kindred’s resources with Gentiva’s home health and hospice capabilities, Diaz said.

Gentiva Shares

Gentiva jumped 51 percent to $12.90 at 8:17 a.m. New York time. The shares had fallen 20 percent in the 12 months through yesterday. Kindred declined 2.9 percent to $21.92 yesterday and has gained 80 percent in the last 12 months.

Gentiva on May 7 reported first-quarter profit of 13 cents a share, beating analysts’ estimates by 2 cents. The company reaffirmed its 2014 forecast of earnings, excluding one-time items, of 85 cents to $1.15 a share on revenue of $1.9 billion to $2.1 billion.

Diaz said Kindred elected to make its proposal known to Gentiva’s shareholders after being rejected.

“We have undertaken extensive efforts and had several private discussions with Gentiva’s management team in an effort to engage Gentiva on a mutually acceptable transaction,” Diaz said in the statement. “Gentiva has indicated repeatedly that it is not willing to discuss a transaction at this time.”

Citigroup Inc. is acting as financial adviser to Kindred, and Cleary Gottlieb Steen & Hamilton LLP is acting as legal adviser.