The European Union stands ready to beef up its border surveillance mission in the Mediterranean if Italy requests and is supplying 13.7 million euros ($15.6 million) to help Rome cope with the migrant influx, the EU's top migration official said Thursday.

"We are ready to respond constructively if Italy identifies the need to step up Operation Triton," Dimitris Avramopoulos said.

He also announced that the Triton border surveillance mission operating in the Mediterranean Sea would be extended until at least the end of 2015.

The mission was launched in November as Italy deals with growing numbers of would-be migrants attempting the perilous sea crossing from Libya headed mostly for the southern island of Lampedusa.

Italy withdrew its search and rescue mission, Mare Nostrum, in December due to heavy costs and because it appeared to be a safety net that encouraged migrants to look for a better life in Europe.

Some 19,500 migrants have been picked up in the Mediterranean since November, according to EU figures. Of those, 5,600 were rescued in January, a 50 percent increase over the same month in 2014.

More are expected in coming weeks and months as the weather improves.

In a new escalation on Sunday, four armed smugglers threatened an Italian Coast Guard motorboat involved in one of several operations that rescued more than 2,000 migrants leaving Libyan shores.

"We cannot turn a blind eye, and we cannot carry on as if it was business as usual," said Avramopoulos.

Triton was meant to operate for only a few months and has just three aircraft and nine ships at its disposal, most of which cannot work in open seas. It has come under increasing criticism for failing to stem the tide of migrants.

In Rome, Italian Foreign Minister Paolo Gentiloni said the EU funding was an initial response to his country's request, and he hopes more assistance will be agreed in Brussels on March 4 at an EU meeting on migration.