Can I Return to the US as a Visitor If I Withdraw My Asylum Application?
This explains the problem (and options) for someone who withdraws a pending asylum application (Form I-589) and then attempts to return to the United States on a visitor visa. It does NOT discuss I-589 withdrawal after a person is in Immigration Court proceedings.
Immigrant IntentFiling your asylum application told the federal government that you intend to live permanently in the US. Meaning, you have immigrant intent. If you live in Florida, you told the federal government this intent when you filed the application at the Texas Service Center as well as when the case arrived at the Miami Asylum Office.
If a Customs and Border Patrol officer (at the airport on return) believes you have immigrant intent, you will not be allowed to enter the United States on a visitor visa. This includes a visitor for business purposes.
Option One - Get Permission to LeaveThe better option might be to request Advance Parole. If it is an emergency, I suggest applying directly with the local office, such as the Oakland Park Field Office or the Miami Field Office. Take medical documents for yourself or your family members demonstrating a need to travel abroad. The Advance Parole may be issued for up to one year.
Option Two -- Get Permission to ReturnIf you believe you will need to return to the US for business purposes, get permission in the form of a business visa. Professionals on H-1B visas and multinational managers and executives on L-1A visas can travel to the United States even with immigrant intent.