Italy’s prime minister has said that European countries must work together “to stop departures [from Africa]” and swiftly deport those turned down for asylum, who she said “threaten the future of Europe”, after thousands of people seeking refuge arrived on Lampedusa in the last week.

Giorgia Meloni toured the tiny Sicilian island, which for years has been the first port of call for people making the treacherous journey by sea from north Africa, on Sunday morning alongside Ursula von der Leyen, president of the European Commission.

The three-hour visit, which included a stop-off at an overcrowded reception centre and a site near the port that contains the remains of flimsy boats used by migrants, came after almost 8,500 people landed within three days last week – more than the island’s population of 6,000.

The body of a baby who died shortly after being born onboard a boat carrying 40 passengers was placed in a white coffin and taken to the island’s cemetery on Saturday morning. Last week, a five-month-old boy drowned during a rescue operation.

In recent days, there were chaotic scenes at the reception centre, which has the capacity to host only 400 people, with migrants sleeping on the rubbish-strewn street outside and others trying to escape over a fence.

But by the time Meloni and Von der Leyen arrived, the majority had been transferred off the island to centres in Sicily or mainland Italy and the area around the centre made to look almost pristine.

Meloni, whose far-right government took power last October, said the influx threatened “the future of Europe” and that “serious solutions” were needed, such as cracking down on people smugglers, swiftly deporting illegal immigrants, and moving quickly to implement a deal signed this year with Tunisia.

“If anyone thinks that this crisis we are facing could be just resolved within Italian borders, it would be a very big mistake, because this problem involves everyone and needs to be tackled by everyone,” said Meloni. “I continue to say that we will never resolve it by talking only about redistribution [of migrants] – the only way to resolve it is to stop departures.”

Von der Leyen promised the swift deportation of those who fail to be granted asylum and a crackdown on the “brutal business” of people smuggling. “We will decide who comes to the European Union, and under what circumstances. Not the smugglers,” she said.

She outlined a 10-point plan, including providing Italy with support in processing new arrivals while “exploring options to expand existing naval missions in the Mediterranean, or to work on new ones”. Von der Leyen also urged member states to make use of a mechanism enabling them to voluntarily take in migrants to help ease the burden on Italy.

However, people are continuing to arrive on the island. Most had set off from Tunisia, where in July Meloni and Von der Leyen signed a controversial £105m deal to stem irregular migration. No money has yet changed hands and there has been criticism that the numbers of migrants crossing from Tunisia to Italy has risen almost 70% in the months after the deal, a fact that experts have attributed to the fair weather.

Over 127,000 people – more than double the number over the same period last year – have landed on Italian soil so far in 2023.

“I’m travelling to fulfil my dream, which is to go to England, finish my studies and become a doctor,” said Musa Adam, from Sudan, as he waited to be transferred off the island on Saturday night. He said he had tried to reach Europe by boat from Libya four times but was captured by the Libyan coastguard and imprisoned.

“We were beaten,” he said. “I saw friends die of disease and hunger.” He then crossed the desert to Tunisia, where “there are no jobs and no houses – we slept on the street … I have overcome so many challenges already, but I need to stay positive and keep going.”

The latest crisis has reignited a debate over the division of responsibility among EU states and raised questions about the feasibility of deals with north African countries.

Lampedusa, which lies closer to Tunisia than Sicily, has been dealing with migration from north Africa for over 30 years. But patience on the island is wearing thin. Residents have protested over fears that it would turn into a “tent city”.

“We hate to see people suffering and have always been there to pull bodies from the sea or provide food and clothing,” said Giorgia Pirotta. “But we can’t live like this any more. These people deserve respect, and so do we.”

Meloni, whose election pledge was to stop illegal immigration, is hoping the deal with Tunisia can provide a solution. The EU has insisted that the budget allocated to Tunisia would be paid out – it is currently refitting 17 vessels for the Tunisian authorities to use in search and rescue operations.

However, a group of MEPs from the European parliament were refused entry to the country, raising fresh concerns about President Kais Saied’s commitment to address questions of human rights abuses. He has previously declared that Tunisia would not be Europe’s border guard.

The EU migration pact was driven by Meloni, but is backed by the rest of Europe, where migration is seen as a critical issue in elections, particularly those looming in Poland and the Netherlands.

A further £150m is available under the deal with Tunisia to help with economic reforms and develop industrial ties with Europe including green energy.