In an interview published in several European newspapers, EFSF chief Klaus Regling said preparations had been made to help Italy if the current turmoil continued.
"If a country comes and says it needs help immediately, we're ready," Regling was quoted in the German daily Süddeutsche Zeitung as saying.
Nevertheless, time was "running out" for Italy, the EFSF chief said. "The country needs a functioning government as soon as possible."
The sharp volatility seen on the markets was making it difficult to raise the firepower of the €440-billion ($598 billion) rescue fund to the €1 trillion that the bloc's leaders had hoped for, the Wall Street Journal and theFinancial Times quoted Regling as saying.
Investors have fled from bonds issued by highly indebted countries, he told the FT.
Luring them back by offering insurance on losses - the centrepiece of a plan agreed in Brussels on October 26 - would now probably use up more of the funds resources, Regling said, according to the FT article.
"The political turmoil that we saw in the last 10 days probably reduces the potential for leverage," he said. "It was always ambitious to have that number, but Im not ruling it out."
The Wall Street Journal quoted Regling as saying there were not likely to be large, up-front commitments, and that many potential investors would want to know which country or countries need help before putting cash into the new vehicle.
"Don't expect that there will be a few hundred billion sitting somewhere in December waiting to be used for our new instruments," Regling told the paper.
However, he added that it was not necessary to have such a sum in place and that the fund should be able eventually to raise what it needs.
For the EFSF to step in and help Italy, Rome would have to submit a corresponding request to the so-called euro group and if they and the European Central Bank agreed, a number of different instruments would be made available, the Süddeutsche Zeitung quoted Regling as saying.
The instruments included market purchases of new or already issued bonds or the provision of credit lines, but any assistance would be tied to strict conditions, he insisted.
Regling said the EFSF could currently make €250 billion-€300 billion available in loans, since some of its current firepower of €440 billion had already been reserved for Ireland, Portugal and Greece. The fund would begin issuing short-term bonds in December, he said.
"We can borrow a lot of money from short-term bonds" with maturities of three, six and 12 months, he said.
The funds raised would be used to intervene quickly in the markets and buy up the bonds of countries in difficulty or recapitalise banks, he explained.