Andy Jassy, chief executive officer of web services at Inc.

Patrick T. Fallon | Bloomberg | Getty Images

Andy Jassy, chief executive officer of web services at Inc.

Amazon’s behemoth cloud division has swallowed eight or nine companies in the past few years — and it would buy up even more if not for Silicon Valley’s sky-high valuations, the top executive said.

Andy Jassy, Amazon’s highest-paid executive and head of Amazon Web Services, told CNBC’s Jon Fortt that Amazon is more rigorous than rivals when it comes to M&A.

“You know, most of them have been relatively small acquisitions. They’ve been great teams and great technology,” Jassy said. “We’d like to do more. I think there’s two things that sometimes give us pause. One is, we tend to be a little bit more rigorous maybe than others choose to be in our analysis and valuations. And sometimes the valuations that are out there just haven’t matched what we can kind of get our heads around.”

Amazon’s cloud business leads the rest of the market considerably — it had about 44 percent market share in 2016, according to Gartner’s “infrastructure as a service” estimates. And when AWS goes down, much of the internet crashes with it.

But Jassy’s remarks reflect a growing trend of caution in Silicon Valley, even for companies as rich as Amazon, as more and more start-ups reach “unicorn” valuations of $1 billion or more.

“I’m not passing judgment,” Jassy said in an interview that aired on Tuesday. “We have a history, and confidence, in being able to build ourselves. And so at a certain point, if we know customers really want something, and we’re looking at something that we believe can accelerate our efforts in that area — but we just can’t get our heads around the valuation or it’s not the right fit — then we’re also not afraid to go hire people and build it.”