CHICAGO — Netflix Inc., focused on building its online streaming library of more than 20,000 titles, said Monday that it signed a deal with Miramax Films that will give its users access to movies such as “Pulp Fiction,” “Good Will Hunting” and “The English Patient,” beginning in June.

Financial terms of the multiyear deal were not disclosed. This is the first time that Miramax titles have become available to any digital subscription service.

Over the past year, Netflix has set up content deals with Walt Disney Co., CBS Corp., the premium movie channel Epix and 20th Century Fox. Fox is owned by News Corp., which also owns MarketWatch, the publisher of this report.

Online streaming has become the fastest-growing source of new customers for Netflix, which now has almost 24 million subscribers.

While the video rental provider has a DVD and Blu-ray library of well over 120,000 titles, it has been working to improve its catalog of streamed content to keep up with ever-rising expectations among investors.

Analysts worry that the video-on-demand content offered by cable companies like Time Warner Cable Inc. and Comcast Corp., along with the streaming products from Amazon.com, Hulu Plus and other new entrants, will slow down Netflix’s growth. Already, the stock, priced at more than 70 times its earnings, was punished last month when Netflix issued a second-quarter outlook that fell short of many forecasts.

Some also fear that the company’s deals with the studios will become too expensive, but Netflix founder Reed Hastings has stressed that the company will not spend at a rate that will prevent it from having an operating profit margin of at least 14 percent.