The Philippines is considering pulling troops back from a guerilla camp where three International Committee of the Red Cross (ICRC) hostages are being held.
But the interior secretary of the Philippines, Ronaldo Puno, rejected the kidnappers' demands for a full army withdrawal from the area on the southern island of Jolo.
"We will not surrender the entire island to the capricious demand of the kidnappers," he said, adding that there would be no ransom payments either. "If we do this, everybody outside this area becomes a potential kidnap victim."
The hostages, a Swiss, an Italian and a Philippines national working for the Geneva-based ICRC, were captured on Jolo in mid-January.
Abu Sayyaf militants have threatened to behead one of the hostages unless the government allows them to move more freely on the island and withdraws security forces from a cordon set up around their stronghold by Tuesday.
Jolo Governor Satur Tan said repositioning the troops several kilometres away could allow the negotiations to continue, but that the government would not give the militants too much space to manoeuvre.
The ICRC said it was "extremely concerned" for the hostages' safety and urged the military on Thursday to consider the withdrawal demand.
The United States-backed military, which has been battling the Abu Sayyaf for more than a decade, had earlier rejected a troop withdrawal, saying the militants could not be trusted.
swissinfo with agencies