Google Inc., the maker of Android software for mobile phones, said it will stop supporting the Gmail application for rival BlackBerry smartphones, made by Research In Motion Ltd.

The app for Google’s Web-based e-mail will no longer be available as of Nov. 22 and won’t be supported after that, the Mountain View, California-based company said in a blog posting. Users may continue to use the app if already downloaded, Google said.

For consumers with a Gmail account who want to access those messages on the go, the move may give them reason to not opt for a BlackBerry when buying a new device. It is a setback for RIM which is struggling to find ways to stop a decline in smartphone market share as customers increasingly opt for Android devices or Apple Inc.’s iPhone.

RIM’s share of the global smartphone market fell 5 percentage points to 10 percent in the third quarter from a year earlier, according to research firm IDC. Its market share in the U.S. alone dropped to 9 percent from 24 percent, according to another researcher Canalys.

Google said it is stopping development of its app for BlackBerrys to focus on the mobile browser experience, without elaborating further.

RIM fell 2.1 percent to $18.44 at 11 a.m. in New York. Before today, the stock had dropped 68 percent this year. Google fell 0.8 percent to $607.37.