* As many as 30 migrants found suffocated or drowned
* Italian navy rescued more than 5,000 people over weekend
* Migrant influx stokes anti-immigration sentiment (Adds comments from Luxembourg foreign minister)
By Isla Binnie
ROME, June 30 (Reuters) - As many as 30 corpses were found on a boat packed with migrants off the coast of Sicily, Italy's navy said on Monday after rescuing thousands of people trying to cross from North Africa over the weekend.
The dead are thought to have either suffocated on the overcrowded fishing vessel or drowned, the navy said.
The discovery on Sunday underlined the scale of the crisis in the southern Mediterranean, where hundreds have died in the past year making the journey to Europe, and tens of thousands more have been plucked from rickety boats.
More than 5,000 people were rescued this weekend, adding to the 50,000 migrants who have reached Italy from North Africa so far this year, many fleeing war and forced conscription as well as poverty and a lack of opportunity.
Italy has called on its European Union partners to do more to help manage the near daily arrivals, a phenomenon that has boosted voter support for the anti-immigration Northern League party in a country struggling to emerge from recession.
"We can't leave Italy and maybe Malta isolated. It's a European problem," Luxembourg Foreign Minister Jean Asselborn said on a visit to Rome, noting that EU interior ministers were due to meet in Milan next week.
"We may be able to work on finding a more appropriate solution," he said.
The breakdown of order in Libya has made it virtually impossible to control the boats departing and, at the current rate, the figures should soon pass the record of 62,000 people who arrived by sea in 2011, the year of the "Arab Spring" turmoil across North Africa and the Middle East.
An Italian ship from the navy's migrant rescue mission Mare Nostrum, or "Our Sea", was due to arrive at the Sicilian port of Pozzallo on Tuesday towing the fishing boat and carrying 566 survivors.
The navy said thousands of others rescued this weekend would arrive in other ports on Monday and Tuesday.
Prime Minister Matteo Renzi said last week the EU should take responsibility for rescuing migrants by investing more in regional border control agency Frontex.
Renzi has also urged the United Nations to intervene in Libya, where traffickers charge migrants more than $1,000 each for the risky passage.
European Home Affairs Commissioner Cecilia Malmstrom said the commission was making available to Italy 4 million euros ($5.5 million)of emergency funding and was looking at ways to contribute more.
"This new death toll clearly illustrates that smugglers and criminals have no respect for human lives and we must urgently increase our efforts to fight their deadly activities," Malmstrom said.
Northern League leader Matteo Salvini, whose party says Mare Nostrum is a burden on taxpayers and encourages immigration, attacked Renzi and Interior Minister Angelino .
"Thirty more deaths on the consciences of those who defend 'Their Sea'. Stop the departures, help them at home, now! Renzi and Alfano have blood on their shirts, don't they?" he said on Facebook.
Mare Nostrum is Europe's biggest search and rescue mission and costs around 9 million euros a month. ($1 = 0.7331 Euros) (Additional reporting by James Mackenzie; Editing by Robin Pomeroy)