There is a very easy way to do that. You can run FitNesse tests from the command line. You do this by using the following command line:
java -jar lib/fitnesse.jar -c "FrontPage?suite&format=text"
This will run all tests under the FrontPage and show the results as they happen in a command line friendly format. If you change FrontPage to FrontPage.MainSuite, it will run only the tests under that page.
If you have tests that are in different states. Maybe some of them are started but are not done yet. You can add a Suite Tag to the tests that must run, then you can filter the tests that are run. that would look like the following:
java -jar lib/fitnesse.jar -c "FrontPage?suite&suiteFilter=MustBeGreen&format=text"
This is also possible to do using an ANT java task.
Assuming you have a current version of fitnesse and have it running on port 8080, the following link will take you to a page with more details: http://localhost:8080/FitNesse.UserGuide.ControllingFitnesseFromTheCommandLine