I submitted my asylum application to U.S. Citizenship and Immigration Services (USCIS) five months ago and I was recently invited to my friend's wedding in Canada this summer. I am scheduled for my asylum interview next month, and I know I won't have a decision before then, but I was wondering if it was okay to travel outside the U.S. for a brief period of time?
Technically, asylum applicants CAN travel outside the U.S., but it's usually not a good idea. Even with your pending asylum application you will be subjected to questioning from Customs and Border Protection (CBP) when you attempt to return to the United States. If you have inadmissibility grounds that could be triggered when you leave (such as unfavorable immigration or criminal history), you may be denied reentry, even if you have the necessary travel documentation. You should consult an immigration attorney who can best advise you to whether it is in your best interest to leave the United States.
If you decide to travel anyways, you will need to submit Form I-131, Application for Travel Document to USCIS in order to receive "advance parole" (permission to reenter the U.S. before your application is approved).
To learn more about this, see Filling Out Form I-131 for Advance Parole. Apply for advance parole well in advance of your trip and make sure you do not leave the U.S. without your travel document.
The biggest travel "don't" for asylum applicants is returning to the country where you have indicated that you fear persecution. If you do so, USCIS will then presume that you have abandoned your asylum application and may even decide that you submitted a fraudulent application—which could have serious consequences such as a permanent bar from reentering the United States.