A U.S. judge has declined to ban Apple's (AAPL.US) lucrative search agreement with Alphabet (GOOGL.US), a deal that generates approximately $20 billion in annual revenue for the iPhone maker, sending Apple shares higher in after-hours trading.

While Judge Amit Mehta ruled in an antitrust case that Alphabet cannot enter into exclusive internet search agreements, he permitted the company to establish default search engine agreements with browser developers. "Alphabet is allowed to pay fees to browser developers such as Apple," he wrote in his ruling.

However, Mehta stipulated that partner companies must promote alternative search engines, provide options under different operating systems or privacy modes, and allow annual changes to default search engine settings. "Cutting off Alphabet's payments would almost certainly cause significant harm to distribution partners, related markets, and consumers, and in some cases even devastating downstream damage, so a broad payment ban should not be implemented."

Apple currently shows preference for Alphabet's search engine by giving it prime placement in Safari search bars on computers and mobile devices. Users can choose to switch to other options such as Microsoft's Bing or DuckDuckGo. Apple also modified its iOS software two years ago to allow different search engines in privacy mode.

Apple shares rose as much as 4.3% to $239.50 in after-hours trading, while remaining down 8.3% year-to-date through the close. Alphabet shares also gained, rising as much as 8.7%.

Apple's search partnership agreement is central to the U.S. Department of Justice's landmark lawsuit against Alphabet. Tuesday's ruling also allows Alphabet to retain its popular Chrome web browser. Mehta ruled last year that Alphabet illegally monopolized web search and search advertising markets, followed by a three-week hearing in April to determine remedies.