Rupert Murdoch's News Corp bought back more than $1 billion of its shares in the last month, according to a filing, as it seeks to improve relations with shareholders frustrated by what they say is the media company's unpredictable capital allocation strategy.

Filings show News Corp, which owns Fox TV, Twentieth Century Fox studios, The Wall Street Journal and The Sun in the United Kingdom, bought back more than 65.6 million Class A shares at between $15.64 and $17.34 in the period from August 15 to September 18.

News Corp shares have risen about 10 percent since July 12, when it announced it would buy back $5 billion in stock over 12 months.

Murdoch's decision to pursue the aggressive buyback strategy was confirmed a day before the company announced it would drop its controversial bid to take full control of UK satellite TV operator BSkyB in the wake of a phone tapping scandal at its UK newspaper unit.

News Corp shares typically trade below the valuations of media conglomerate rivals such as Walt Disney Co and Time Warner Inc . This is because investors take into account a Murdoch discount -- a reference to Murdoch's control and a tendency to make decisions shareholders might not support.

Wall Street analysts and investors have welcomed the aggressive buyback and are hoping for more.

Based on the pace of the repurchases, we expect News Corp to increase authorization for more, possibly by the end of the year, said Collins Stewart analyst Thomas Eagan, who rates News Corp a 'buy' with a $25 price target.

News Corp trades at a discount to its peers because investors feel management isn't shareholder friendly. With this aggressive buyback, they are gradually ameliorating those concerns.

The buyback during the current quarter, which ends September 30 is already the largest in News Corp's history, according to BTIG analyst Richard Greenfield.

(Reporting by Yinka Adegoke in New York; editing by Andre Grenon)