In a defiant audio message that came late Tuesday, hours after Al-Qaeda's Syria affiliate urged an end to clashes between rebels and ISIL, the group's spokesman said it would "crush" opposition fighters.
Abu Mohammed al-Adnani also warned that ISIL considered members of the opposition Syrian National Coalition and the military command of the Free Syrian Army to be "legitimate targets".
The message came after days of fighting between ISIL and a coalition of moderate and Islamist rebels in Syria, and as ISIL battles Iraqi government forces in Anbar province.
The group has seized part of the provincial capital Ramadi and the city of Fallujah.
On the ground in Syria, clashes between ISIL and rebel groups continued in several provinces on Wednesday, with heavy fighting reported in Raqa, the only provincial capital to fall from regime hands.
Overnight, in the nearby border town of Tal Abyad, a car bomb detonated near a rebel headquarters, the Syrian Observatory for Human Rights monitoring group said.
The Observatory said a force of ISIS fighters had withdrawn from Deir Ezzor Tuesday to reinforce the organisation in Raqa.
Elsewhere, the Observatory said 100 ISIL members had surrendered to the jihadist Al-Nusra Front in Aleppo's Salhin neighbourhood.
The Nusra Front, which is Al-Qaeda's official affiliate in Syria, was established in mid-2011 with help from ISIL's Iraqi precursor.
The Iraqi group's chief later sought to merge his group with Al-Nusra, but they rejected the alliance and pledged allegiance directly to Al-Qaeda chief Ayman al-Zawahiri.
Since then, the two groups have functioned separately, though Al-Nusra has remained largely neutral in the latest fighting, according to Observatory director Rami Abdel Rahman.
"In Raqa, a brigade of the Al-Nusra Front that was formerly known as Thuwaar Raqa is fighting against ISIL, but elsewhere in the country Al-Nusra is on the sidelines of the fighting," he told AFP.
On Tuesday afternoon, Al-Nusra chief Abu Mohamed al-Jolani called for an end to the rebel-ISIL fighting, warning it would benefit the Assad regime.
The fighting "risks costing us dearly on the ground if it continues," he said in an audio message.
"The regime will gain new life when it was close to collapse," he added, calling for a ceasefire, exchange of prisoners and the establishment of an Islamic committee to mediate disputes.
He urged all fighters "to give priority to the fight against the regime."
Late Tuesday night, ISIL spokesman Adnani released his own audio message, though it was unclear if it was a direct response to Jolani.
He sounded a defiant tone about the fighting in Syria, urging ISIL forces to "crush them (the rebels) totally and kill the conspiracy at birth."
"None of you will remain, and we will make of you an example to all those who think of following the same path," he added.
Adnani also warned that ISIL had "declared and begun a war" against the opposition National Coalition and the military command of the so-called opposition Free Syrian Army.
"Everyone who belongs to this entity is a legitimate target for us, in all places, unless he publicly declares his rejection of that group and of fighting the mujahedeen (jihadist fighters)."
Adnani's message also urged Sunnis in Iraq to continue fighting government forces.
"Oh Sunni people, you were forced to take up the weapon," he said.
"Do not lay the weapon down, because if you put it down this time, the (Shiites) will enslave you and you will not rise again."
Elsewhere in Syria, an international effort to dismantle the country's chemical weapons programme moved forward on Tuesday, with a first shipment of chemical material removed by sea.
The material was taken from the port of Latakia on a Danish vessel to international waters, where additional material will be gathered and then transported to a US ship for destruction.
Syria has pledged to give up its chemical weapons programme, with a mid-2014 for it to be completely dismantled.
The disarmament deal came after Washington threatened military action against Damascus in response to an August 2013 chemical weapons attack outside the capital that killed hundreds.
AFP