NEW YORK — Cable TV operator Charter Communications intensified its pursuit of the much larger Time Warner Cable and vowed Monday to bring an offer directly to shareholders if needed after getting rebuffed by Time Warner’s management.

Time Warner Cable called the move “a non-starter.”

There have been months of speculation over a cable company buying Time Warner Cable, the nation’s No. 2 cable TV provider behind Comcast Corp. Monday’s pronouncement by Charter represents its most public overture yet, even as financial terms haven’t changed significantly. Although there is no formal proposal on the table, Charter said it is willing to make a cash-and-stock offer that could be worth up to $38 billion.

The developments come as broadcast and pay-TV channels demand higher fees from cable TV operators to include those channels in customers’ cable lineups. Last summer, Time Warner Cable had to drop CBS for about a month because of a fee dispute. The cable company lost more than 300,000 video subscribers in the third quarter.

By combining, Charter and Time Warner Cable could increase their negotiating powers with the TV channels — and perhaps reduce the fee increases they pass on to customers.

The cable companies could also develop better apps for customers to watch channels on phones and tablet computers, as they try to retain customers who are increasingly watching video on the Internet.

Charter Communications Inc., which is based in Stamford, Conn., said it is prepared to bring the offer directly to shareholders after determining there is “no genuine intent” from Time Warner Cable’s management to engage in merger talks. But Charter said it was open to continued talks with New York-based Time Warner Cable first.

Charter said it has made repeated overtures to Time Warner Cable for more than six months. In Monday’s letter, Charter said it was willing to pay in the low $130s per share, including about $83 in cash.