A new survey found that most consumers say they rarely or never mean to click on ads served up on their phones.

Button, a mobile partnership platform that facilitates discovery and transactions for brands, and App Annie, a mobile app data and insights provider, surveyed 1,106 US smartphone users ages 18 to 73. The study found that for the most part, consumers aren't too keen on mobile ads.

Take millennials, for example. More than four in 10 said they rarely click on a mobile ad, and another 17% said they never did.

While there were some (31%) who said they sometimes click on a mobile ad, very few (10%) did so regularly.

This was the case for older consumers as well. In fact, baby boomers were the least likely to engage with mobile ads. Nearly a quarter said they never did, while another 49% said they rarely did so. Just 4% said they clicked on a mobile ad at least somewhat often.

Meanwhile, ads promoting mobile apps tell a somewhat different story. The study found that when it comes to those types of ads, consumers are more engaged than with ads in general. But even that engagement rate is declining.

Some 52% of all respondents said they intentionally clicked on a mobile ad for another app, down from 57% in 2015. And while engagement levels with mobile app ads was relatively high, only 44% of those who clicked on such an ad actually downloaded the app.

That same study from App Annie and Button also found that apps are outdoing the mobile web when it comes to the shopping preferences of US smartphone users. (Read more about that on eMarketer Retail.)

Separate data from the Interactive Advertising Bureau (IAB) conducted earlier this year also took a look at the differences in consumer responses to advertising on the mobile web vs. in-app ads.

Nearly half (47%) of smartphone users polled worldwide said they took some sort of action after seeing an ad in a mobile app, while slightly fewer (45%) did so after seeing a mobile web ad.

When it came to actually clicking on the ad, roughly one in 10 had done so.