Addressing parliament, Foreign Minister Paolo Gentiloni also outlined Italy's readiness to play a leading role in de-arming and rebuilding its former colony in the event of a UN-brokered cease-fire in a conflict that has plagued Libya since the 2011 Western-backed overthrow of Moamer Khadafi.
Gentiloni said there was a serious danger of Isis fighters forging an alliance with local militias or criminal gangs currently engaged in a multi-sided battle for control of Libya.
The country has no functioning government and is headed for bankruptcy because of a collapse in its oil production as a result of the fighting.
Italy sees the chaos as driving the accelerating flux of African migrants trying to reach its shores from Libya.
Time running out
"There is an evident risk of an alliance being forged between local groups and Daesh and it is a situation that has to be monitored with maximum attention," Gentiloni told MPs. Daesh is the Arabic acronym for Isis.
"We find ourselves facing a country with a vast territory and failed institutions and that has potentially grave consequences not only for us but for the stability and sustainability of the transition processes in neighbouring African states," the minister added.
"The time at our disposal is not infinite and is in danger of running out soon."
Gentiloni stressed that Italy was not considering military action along the lines of the airstrikes Egypt has carried out this week in retaliation for Isis's beheading of 21 Egyptian Christians in Libya.
"Saying we are on the front line does not mean announcing adventures nor crusades," he said.
"What we are doing as part of the anti-Daesh coalition in Iraq and Syria is the way a democratic country responds to barbarism and we are doing it in friendship with the vast majority of the Islamic community who refuse to see their faith hijacked."
A total of 5,302 migrants have arrived in Italy from Libya since the start of January, a 59 percent increase on the same period in 2014.
More than 300 Africans have died at sea in the last week alone in what aid workers suspect is a sign of people smugglers trying to get their human convoys out of Libya as soon as possible.
Gentiloni called for Triton, the European Union's limited coastal patrol operation in the Mediterranean, to be expanded to prevent further loss of life.
"The EU is an economic superpower and an economic superpower can go beyond the €59 million a year it is currently spending on an emergency of this scale," he said.
Some opposition figures in Italy have called for all search-and-rescue operations in the Mediterranean to be suspended because of a much-touted risk of terrorists posing as refugees as a way of getting into Italy to stage "lone-wolf" attacks.
The government admits it can't rule out that happening but says screening measures are in place to combat the risk, and that it has yet to find any evidence of Isis attempting this.
The government has also had to contend with a widely-circulated claim that up to 200,000 African migrants in Libya are about to embark or be ordered on to ships for Italy.
Matteo Salvini, the far-right leader of the anti-immigrant Northern League, has been the principal promoter of this claim, for which no reliable evidence has so far emerged.
Gentiloni said Italy was ready to help implement a UN-brokered peace deal in Libya by sending troops to monitor a cease-fire and help with the de-arming of the country and the integration of militia fighters into the regular armed forces.
Italy would also provide medical and reconstruction help and reinstate a cooperation agreement with its former colony that was suspended last year.