* Migrant arrivals up 36 pct this year
* Libya saw heavy fighting this week
* European, African officials to meet in Rome
By Steve Scherer
ROME, March 17 (Reuters) - Italy will host a meeting between European and North African countries next week in a bid to strengthen support for an agreement it struck with Libya to fight people smuggling as migrant arrivals surge.
The prime minister of the U.N.-backed government in Tripoli, Fayez al-Seraj, will meet with Italian Prime Minister Paolo Gentiloni and interior ministers from eight European countries including Germany and France on Monday.
Last month Italy pledged money, training and equipment to help Libya fight people smugglers, a deal that was endorsed by European Union member states.
But Libya is still far from stable. Two governments are vying for power - in Tobruk to the east and Tripoli to the west - and the country remains mired in factional fighting and lawlessness.
The authorities in eastern Libya have rejected the deal struck between Rome and Tripoli.
"I'm not so naive as to not understand the situation there," Italian Interior Minister Marco Minniti told reporters. "But we cannot remain immobile and wait for the country to stabilise."
He said the Libya agreement and next week's meeting were not just "talk", but strategic steps toward managing mass migration to Europe.
So far this year more than 16,000 migrants - a 36 percent increase on the same period last year - have been rescued at sea and brought to Italy after Libya-based people smugglers piled them onto flimsy boats.
As part of the deal, Italy and the EU have promised to fund migrant camps on Libyan soil, but they need U.N. agencies to help manage them. Those same agencies have said Libya is not safe for migrants.
"Migrants and refugees in detention (in Libya) are held outside any legal process and in conditions which are generally inhuman. They are exposed to malnutrition, extortion, torture, sexual violence and other abuses," four U.N. chiefs said in joint statement last month.
On Friday, Italy's opposition 5-Star Movement also took issue with the Libya agreement, calling it "a sham". In a statement, 5-Star lawmakers said Libya was too dangerous for Italy's diplomats, urging the closure of the embassy in Tripoli.
Last week Tripoli was gripped by heavy fighting as armed groups allied with Seraj took over a compound that had been occupied by a rival leader, while forces in Libya's Oil Crescent battled for control of two major oil ports.
EU Migration Commissioner Dimitris Avramopoulos and interior ministers from Algeria and Tunisia will also attend the meeting.
(Reporting by Steve Scherer; editing by Richard Lough)