The Jerusalem district court last month rejected an earlier petition against the decision to expel Omar Shakir, a US citizen, ruling he had until May 1 to leave.
But just a day ahead of the deadline the supreme court issued an injunction allowing Shakir to remain in Israel for seven days, attorney Michael Sfard said.
During this period the interior ministry can submit its response to the appeal which Shakir lodged at the supreme court.
After the May 7 deadline the court "could theoretically issue a new decision" on the case, Sfard told AFP.
The interior ministry's decision to deny Shakir his work and residency permits was due to his alleged support of a boycott of Israel over its treatment of Palestinians - a claim accepted by the district court.
HRW denied the group or Shakir promoted a boycott of Israel, calling the April district court ruling a "new and dangerous interpretation of the law," since it equated criticism of businesses operating in the occupied West Bank to boycotting Israel.
In 2017, Israel passed a law banning entry to foreigners who support boycotting the country.
The law was passed in response to a movement to boycott Israel by those seeking to pressure the country over its occupation of Palestinian territory.
Israel sees the movement as a strategic threat and accuses it of anti-Semitism - a claim activists deny, saying they only want to see the occupation end.
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