BERLIN — From the reed towers of Rome, German Chancellor Angela Merkel called Friday for Europe to embrace the migrant crisis and live up to its long tradition of welcoming the lonely and the poor, saying she believed Europe had “so much to offer.”

In an impassioned farewell speech to young people at the Union of European Students in Rome, Merkel did not seek to mask her disappointment with the wave of migrants crossing into Europe, and nor did she seem to view the wave of refugees flooding across the Mediterranean as a salvation from Europe’s woes.

In all, there have been some 850,000 migrants entering Europe in the past year, including 160,000 who reached Italy alone, according to the International Organization for Migration. Despite repeated agreements between European countries on how to deal with the influx, the deadlock continues. In Germany alone, more than 1 million asylum-seekers arrived between September 2015 and March 2016.

In that short span, Merkel and her allies in the conservative Christian Democratic Union have deeply changed German politics. They have also been the biggest obstacle to a resolution of the crisis, and Merkel’s recent election victory has left her political rivals both bitter and frustrated.

But Merkel’s return to power last month has revived the debate about how Europe should deal with the crisis and whether its long tradition of acceptance and solidarity with refugees, so deeply rooted in the region’s history, is still relevant today.

Merkel, who spoke to several thousand young people from all over Europe in the cavernous Gothic basilica in St. Peter’s Square, offered her own answer.

She told them that “if today European culture is defined by the Church, our Europe is defined by itself” — and that Europe “has been built not only on a market economy but also by the exchange of persons — the exchange of destinies.”

Germany, she said, is “unlike other countries” when it comes to the issue of migration. “We didn’t have to set up a German passport-free travel zone to be a successful country. And yet the Germans, as well as many other European countries, are open to having their rules respected, even at the cost of providing compromises.”

Germany “hasn’t given up its objective, but has adapted, a consensus has been arrived at and is capable of functioning,” she said.

“As an old woman,” she told the crowd, she remembered that “when I was in my teens, I didn’t want to live through the streets of my Berlin neighborhood,” but “by recognizing that our Europe is a society of diversity, I gave up my fear and my fear I gave up the street.”

“Our old continent” now needed to reaffirm that diversity, she said. “We’ll miss you.”

Merkel took the podium shortly after a German delegation led by Vice Chancellor Sigmar Gabriel handed the first refugees in Europe to the Italian government in more than a month to prevent them from reaching beaches in the Mediterranean.

Italian and German officials said as many as 300 people, including a baby and several infants, arrived in Rome from Serbia, a country that had been stopped from sending migrants across the sea because it was not a signatory to a 2014 pact to prevent refugees from heading to Europe.

Migrants in Serbia were hoping that this deal would enable them to continue their journey to travel through Serbia and reach Germany, a European Union member. But the migration deal set up at the end of January called on each of the European states to fulfill its obligations under it for up to 15 days, allowing them to cross the border before being sent back.

The head of the Italian refugee protection agency, Adera, Giancarlo Giorgetti, told German television channel ZDF after the arrival in Rome that there would probably be at least 10 more people who came to Rome. He added that the arrival of 10 people in one day was an example of what would likely happen over the weekend.