USCIS guidance says a person with refugee or asylum status who needs a Refugee Travel Document should file Form I-131 before leaving the United States. USCIS has also recommended filing well in advance of planned travel.
Do not assume you can simply apply after leaving
USCIS guidance describes limited discretion for certain applications made while a person is already abroad, but a traveler should not rely on that exception. Filing before departure also allows USCIS to schedule required biometrics in the United States.
Biometrics matter
USCIS states that if a person files Form I-131 in the United States and leaves before required biometrics are collected, the application may be denied. Read the current notice and instructions before making travel plans.
A travel document does not guarantee entry everywhere
A Refugee Travel Document concerns travel and return documentation under U.S. immigration rules. Another country may have separate visa or entry requirements.
Travel connected to the country of claimed persecution
Travel to the country from which a person received refugee or asylum protection can raise serious questions. Form I-131 itself asks about return travel and certain contacts with that country. Get individualized legal advice before making such travel plans.
Keep a complete travel record
Save the filed I-131, receipt, biometrics notice, approval, copy of the issued travel document, itinerary, and records of departure and return.
Official source
This article provides general information and is not a determination that a particular person should travel.