* Minister says "strong action" needed to stop shipwrecks
* Hundreds drowned in boat disasters last week
* Italy and Malta want more funds from EU
By James Mackenzie
ROME, Oct 13 (Reuters) - Italy is to step up naval and air patrols in the southern Mediterranean to try to prevent repeats of the shipwrecks which have drowned hundreds of African migrants in two separate disasters in little more than a week.
Prime Minister Enrico Letta said late on Saturday an "air and naval package" would be put in place south of Sicily, where tens of thousands of migrants in flimsy, overcrowded boats have made the crossing from Africa so far this year.
At least 34 people drowned on Friday when their boat overturned, according to the Italian navy, but with many unaccounted for, the true total could be as high as 200 or more.
In a separate shipwreck on Oct. 3, more than 350 died.
Survivors of Friday's wreck reported their vessel had been fired on as they left Libya, said Barbara Molinario, spokeswoman for the United Nations High Commissioner for Refugees.
"Survivors told us that shots were fired at the boat as it took to the sea," she said. "Three people were wounded and the boat was damaged in such a way that it took on water."
She said the survivors said the shots were fired by "Libyans" but it was not possible to identify them more closely.
Libyan Prime Minister Ali Zeidan denied Libyan forces were involved but promised to investigate.
The incident underlined the chaotic conditions in Libya, the departure point for many migrant boats. The central government is struggling to impose its authority on armed militia groups.
Italian officials have been increasingly worried by the uncontrolled surge in arrivals from a region also destabilised by civil war in Syria and unrest in Egypt and elsewhere.
"We intend to triple our presence, in terms of both men and means in the southern Mediterranean, for a military-humanitarian mission that has been made necessary in part by the fact that Libya is currently a 'non-state'," Defence Minister Mario Mauro told the Catholic daily Avvenire.
"We need strong action to stop these shipwrecks out to sea."
He said operational and financial details of the deployment were being worked out and could involve more patrol vessels or more powerful ships with greater surveillance capacity. Italian media reported that unmanned drone aircraft based in Sicily could also be used to identify boats in trouble.
In addition to coastguard and frontier police vessels, the Italian navy currently has three vessels supported by four helicopters patrolling the area, and two surveillance aircraft with night vision capabilities in support.
Italy and Malta, points of arrival for most of the migrants from North Africa, have asked for more funds from the European Union and called for the migrant emergency to be put on the agenda of the next European Council meeting on Oct. 24-25.
"The fact is that as things stand, we are just building a cemetery within our Mediterranean Sea," Malta's Prime Minister Joseph Muscat said in an interview with the BBC.
Libyan Prime Minister Ali Zeidan backed calls for more action from Europe following a meeting with Muscat in Tripoli on Sunday, but the Maltese prime minister said no real progress would be made until order was restored along the African coast.
"To have a permanent solution or at least a better way of dealing with the issue of illegal emigration, there needs to be stability in Libya," he said.
Italian and Maltese vessels recovered 34 bodies and picked up 206 survivors on Friday after their boat capsized.
But according to survivors' estimates gathered by United Nations officials, the boat had been carrying as many as 350-450 people, meaning the real death toll could be over 200. "At this stage it's impossible to say for certain," Molinario said.
The incident came just over a week after more than 350 Eritreans and Somalis drowned off the island of Lampedusa.
On Sunday, Italian vessels rescued about 400 people from a struggling boat around 60 miles (100 km) south of Lampedusa while another boat carrying around 100 was picked up by Maltese rescuers, an Italian coastguard official said.
U.N. Secretary General Ban Ki-moon said the international community had to address the root causes of the crisis.
The deaths have set off a fierce political debate in Italy over tough rules intended to combat clandestine immigration which make it an offence to offer help to illegal migrant boats.
Letta said on Saturday he favoured changing the law but he faces stiff opposition from centre-right partners in his left-right coalition government who insist the law should stay.
Instability in North Africa and the Middle East has removed many controls which used to prevent boats setting out, and Europe has struggled to come up with a comprehensive response.
European Home Affairs Commissioner Cecilia Malstrom has called this week for Europe's frontier agency Frontex to be strengthened to be able to deploy search and rescue operations.