She made her comments as she was joined on the island for crisis talks by European Commission President Ursula von der Leyen, who insisted “we are in this together”.
But Sky News’ international correspondent John Sparks reported the area had been “sanitised” for the visit and the chaotic, overcrowded reception centre cleaned and cleared of many migrants.
TV images showed Ms Meloni speaking to islanders expressing their frustrations with the current situation.
She told them the government was working on a robust response, including a €50m (£43m) to help the island, but a heckler in the crowd said it was not just money needed.
In the face of the current emergency, Ms Meloni has pledged tougher measures and renewed calls for a naval blockade of North Africa to stop the boats from getting through – after a newborn baby was found dead on a migrant boat.
Speaking at a news conference, she said: “I would like to repeat that I do not consider this a gesture of solidarity of Europe towards Italy, I consider it instead a gesture of responsibility of Europe towards itself because these are the borders of Italy but they are also the borders of Europe.”
Ms Meloni added: “If someone in Europe thinks that facing the global crisis that we are facing, the question could simply be resolved by closing it inside the Italian borders, they would clearly be blind.”
Advertisement
Please use Chrome browser for a more accessible video player
0:14
Meloni answers question from Sky News
Ms von der Leyen said: “Irregular migration is a European challenge and it needs a European answer, so we are in this together.
“Prime Minister Meloni and I are here today to offer a coordinated response by the Italian and European authorities.
“I want to be very clear we have an obligation as part of the international community. We have fulfilled it in the past and we will do so today and in the future.
“But we will decide who comes to the European Union and under what circumstances.”
The problem has become a major headache for Ms Meloni, whose right-wing government has pledged to curb illegal immigration.
Nearly 126,000 migrants are reported to have arrived in Italy this year, almost double the figure by the same date in 2022.
It has parallels to the situation facing the UK in stemming migrant crossingsfrom France, with Rishi Sunakunder pressure to deliver on his “stop the boats” pledge.
The Labour leader, Sir Keir Starmer, told Sky News on Sunday Tory claims about his party’s plans to stop illegal boat crossings were “complete garbage” – with the issue set to be an election battleground next year.
Lampedusa – closer to Africa than the Italian mainland – has recently borne the brunt of crossings from Tunisia, which has replaced Libyaas the main migrant smuggling base.
More than a dozen people are missing after a tourist boat sank in the Red Sea off the coast of Egypt, officials have said.
The boat, Sea Story, was carrying 45 people, including 31 tourists of varying nationalities and 14 crew.
Authorities are searching for 17 people who are still missing, the governor of the Red Sea region said on Monday, adding that 28 people had been rescued.
The vessel was part of a diving trip when it went down near the coastal town of Marsa Alam.
Officials said a distress call was received at 5.30am local time on Monday.
The boat had departed from Port Ghalib in Marsa Alam on Sunday and was scheduled to reach its destination of Hurghada Marina on 29 November.
Some survivors had been airlifted to safety on a helicopter, officials said.
It was not immediately clear what caused the four-deck, wooden-hulled motor yacht to sink.
The firm that operates the yacht, Dive Pro Liveaboard in Hurghada, said it has no information on the matter.
According to its maker’s website, the Sea Story was built in 2022.
Russia launched a large drone attack on Kyiv overnight, with Volodymyr Zelenskyy warning the attack shows his capital needs better air defences.
Ukraine’s air defence units shot down 50 of 73 Russian drones launched, with no immediate reports of damage or injuries as a result of the attacks.
Russia has used more than 800 guided aerial bombs and around 460 attack drones in the past week.
Warning that Ukraine needs to improve its air defences, Ukrainian President Volodymyr Zelenskyy said: “An air alert has been sounded almost daily across Ukraine this week”.
“Ukraine is not a testing ground for weapons. Ukraine is a sovereign and independent state.
“But Russia still continues its efforts to kill our people, spread fear and panic, and weaken us.”
Russia did not comment on the attack.
More on Russia
Related Topics:
It comes as Russian media reported that Colonel General Gennady Anashkin, the commander of the country’s southern military district, had been removed from his role over allegedly providing misleading reports about his troops’ progress.
While Russian forces have advanced at the fastest rate in Ukraine since the start of the invasion, forces have been much slower around Siversk and the eastern region of Donetsk.
Russian forces have reportedly captured a British man while he was fighting for Ukraine.
In a widely circulated video posted on Sunday, the man says his name is James Scott Rhys Anderson, aged 22.
He says he is a former British Army soldier who signed up to fight for Ukraine’s International Legion after his job.
He is dressed in army fatigues and speaks with an English accent as he says to camera: “I was in the British Army before, from 2019 to 2023, 22 Signal Regiment.”
He tells the camera he was “just a private”, “a signalman” in “One Signal Brigade, 22 Signal Regiment, 252 Squadron”.
“When I left… got fired from my job, I applied on the International Legion webpage. I had just lost everything. I just lost my job,” he said.
“My dad was away in prison, I see it on the TV,” he added, shaking his head. “It was a stupid idea.”
In a second video, he is shown with his hands tied and at one point, with tape over his eyes.
He describes how he had travelled to Ukraine from Britain, saying: “I flew to Krakow, Poland, from London Luton. Bus from there to Medyka in Poland, on the Ukraine border.”
Russian state news agency Tass reported that a military source said a “UK mercenary” had been “taken prisoner in the Kursk area” of Russia.
The UK Foreign Office said it was “supporting the family of a British man following reports of his detention”.
The Ministry of Defence has declined to comment at this stage.