The phrase 'on the territory' is correct and usable in written English.
You could use it to refer to an area or region, such as: The initiative is only available on the territory of New York State.
The inspections will only take place on the territory or in the territorial waters of EU states.
The first one is a clear provision on the territory where the rules apply.
If there is already metastatic cancer on the territory of Stavropol region, one has to take appropriate preventive measures".
It was then one of the only big cities on the territory of future Yugoslavia, together with Belgrade and Sarajevo.
The Nagorno-Karabakh conflict is one of the oldest and bloodiest conflicts on the territory of the former Soviet Union.
World War I bore heavily on the territory.
Now your religious congregation is not necessarily on the territory you are living on.
This tendency continues, and its impact on the territory has been devastating.
Nor has the alliance held land drills on the territory of any of its new members.
"And, of course," he added, "they will seek refuge on the territory of Tajikistan.
"Its effects apply on the territory of a foreign country and are discriminatory," Mr. Cordos added.
