Some large online publishers are expressing initial wariness about Google’s (NSDQ: GOOG) new “search within a search” feature, which some feel could diminish their role in directing users around their sites, according to the New York Times. Google’s new service is touted as a way to help users find specific items within sites like Wikipedia, NYT.com, WashingtonPost.com, Wal-Mart (NYSE: WMT), among many others. When a user enters a search on Google for one of those kinds of sites, Google then offer another search box that lets users to seek out subjects within those sites.

The main issue: the second search box has a Google ad, the revenues of which are not shared with publishers of the sites in question. On top of that, the second search box will occasionally promote a rival’s site. For the most part, though, web publishers are concerned that the second search keeps users on Google-sponsored pages rather than directing them around their own sites. One example cited by the NYT showed a search for the “Washington Post” that took users to the site. When a second search within the WaPo site for “jobs” brought up the newspaper’s classified page, the search box sported ads for Monster.com and CareerBuilder.

Google concedes that it has received at least a few complaints and has turned off the function for those sites, but didn’t identify them. Google also isn’t saying how many sites feature the new search tool. However, the NYT suggested that once the second search function is gone, websites might not be allowed to bring it back later. That could be a problem if the service gains popularity and users start to expect it.

With that in mind, others say that media companies should reconsider their initial hostility to the new Google service. Forbes.com CEO Jim Spanfeller, for one is impressed by Google’s expanded search tool and seems to feel that publishers’ fears are slightly overblown: “Not to be cavalier about it, but sites like The Post and Forbes, which have strong enough brand names, won’t lose more than a very small percentage of people who will go to other sites.”