I have a rental property (with mortgage) in another country. This year is my first year reporting tax in the US, should I report the property abroad as an asset?

You should report the property income and expenses on a Schedule E.  As part of that you will include the property as a depreciable asset.  TurboTax will walk you through the steps.

For more information, please see this TurboTax article:  Where do I enter income and expenses from a rental property?