* Boat carrying 137 migrants reaches Lampedusa
* Italian government set to back increased sea surveillance
* PM Letta says Mediterranean cannot be "sea of death" (Adds Italian, Finnish PM comments)
By Roberto Landucci and Steve Scherer
ROME, Oct 14 (Reuters) - A migrant boat carrying 137 people reached Italy from North Africa on Monday as the Italian government prepared to launch new naval and air patrols to prevent repeats of shipwrecks which have drowned hundreds of Africans this month alone.
The boat docked early on Monday in the port of the southern island of Lampedusa, and the refugees, mostly Syrians, were in good condition, a coastguard spokesman said.
Separately, more than 200 migrants arrived in ports in eastern Sicily after being rescued on Sunday by an Italian merchant ship and by a coastguard cutter.
The arrivals follow the deaths of more than 350 people, mostly Eritreans, in a shipwreck in the area on Oct. 3. Last Friday, at least 34 more migrants drowned when their boat capsized, though the true figure may be above 200.
Lampedusa, which lies southwest of Sicily and just 70 miles (113 km) from the coast of Tunisia, has been a stepping stone for migrants seeking a better life in Europe for two decades.
Now the Syrian civil war and unrest in Egypt and other Arab and African countries are fuelling the flow of refugees, many of whom have to pass through an increasingly unstable Libya.
Italian Prime Minister Enrico Letta's government was due on Monday to endorse plans to ramp up its surveillance capacity in the Mediterranean from Tuesday to try to prevent more deaths.
Letta said Italy must act quickly. Libyan Prime Minister Ali Zeidan, who was kidnapped for several hours last week, has sought Europe's help to stem the migrant flow.
"We can't allow the Mediterranean to be a sea of death," Letta said after meeting his Finnish counterpart Jyrki Katainen in Rome. "We have to act right away because lives are at stake."
Katainen pledged to furnish ships, logistical aid and training to bolster the reach of EU border agency Frontex.
Defence Minister Mario Mauro said on Sunday Italy would triple its presence in the area. Some newspapers said unmanned drone aircraft based in Sicily could be used to identify the flimsy and overcrowded migrant vessels.
Instability in North Africa and the Middle East has removed many controls which prevented boats from leaving.
"Border control is impossible," Zeidan said in a Monday interview with Italy's la Repubblica newspaper.
"We need Europe's support to control the borders, to train our personnel, to use satellites to keep track of these flows. It's a phenomenon that is much bigger than the capabilities of a single state."
European Commission President Jose Manuel Barroso was heckled on Lampedusa last week by islanders who said the EU was partly responsible for the Oct. 3 shipwreck.
Italy and Malta, the main points of arrival for most migrants from North Africa, have asked for more EU funds and have called for the migrant emergency to be put on the agenda of the next European Council meeting on Oct. 24-25.
Italy, deep in recession and pressed by EU budget rules to curb public spending, has received more than 30 million euros to help its overwhelmed immigration centres.
European Home Affairs Commissioner Cecilia Malstrom has called for Frontex to be strengthened to be able to deploy search and rescue operations in a zone from Cyprus to Spain. (Editing by Mike Collett-White)