The leaders of Italy and France have urged the European Union to set up asylum processing centres in Africa to prevent refugees and migrants from undertaking the journey across the Mediterranean.

French President Emmanuel Macron and Italy’s new populist Prime Minister Giuseppe Conte met in Paris on Friday in a bid to bury the hatchet after a bitter diplomatic squabble erupted this week over Rome’s refusal to accept the Aquarius, a refugee and migrant rescue ship, at its ports.

“We should create European centres in the countries of departure,” Conte told a press conference, referring to African nations that have seen an exodus towards Europe in recent years.

His comments were echoed by Macron, who told reporters he supported the idea of “branches of our asylum agencies to tackle this question on the other side” of the Mediterranean.

The two leaders also called for changes to the European Union’s asylum rules, which put the migrant burden on their port of entry to Europe – mainly Italy and Greece.

Conte singled out the Dublin regulations, under which the EU country where an asylum seeker first arrives must deal with their application, as needing change.

“The very concept of a state of first entry needs to be rethought,” he argued. “Whoever sets foot in Italy sets foot in Europe.”

“We are drafting our own proposal,” said Conte, adding that it will be presented during the Austrian presidency of the European Council beginning next month.

Macron urged greater solidarity with Rome over the migrant crisis, calling for “profound reforms” of the Dublin regulation.

There have been few signs that European leaders are ready to coordinate their policies despite a looming end-of-June deadline to change the EU’s current asylum rules.

In Germany, Europe’s biggest economy, Chancellor Angela Merkel is embroiled in a showdown with the right wing of her governing coalition, which is demanding that she immediately ditch her liberal migration policy and tighten border controls.

On Wednesday, Germany’s Interior Minister Horst Seehofer said Austria and Italy should ally themselves with Germany to work at the interior minister level on security and immigration.

“Merkel is very much against starting to send people back … but it’s clear her interior minister … wants to do that,” Al Jazeera’s Nadim Baba, reporting from Paris, said.

“She [could] be forced into a situation where she would have to sack him; [if so] her government would collapse and probably she would no longer be chancellor, so she is desperately trying to come to some sort of agreement which involves other countries,” he added.

In Paris, both Macron and Conte slapped down an “axis of the willing” proposed this week by hardliners such as Conte’s own interior minister, Matteo Salvini, and Austrian Chancellor Sebastian Kurz, who says he also has the support Seehofer.

“I would want an axis of the willing comprising all European countries,” Conte said.

Macron said that any decisions on joint migration policy involving France, Germany and Italy would be taken by their respective presidents and prime ministers.

Terms such as “axis” “have never brought us anything good in the past,” Macron remarked, before suggesting that Salvini’s links with fellow migration hardliners might be put to better use persuading them to help Italy deal with its arrivals.

“So, if Austria, Hungary and some others, thanks to these special contacts, can provide more of the solidarity that Italy needs, it’s very good news for Italy and for everyone,” Macron said.

Speaking alongside Macron in Paris, Conte said the two had “fully clarified” their views and were in “perfect agreement”.

The spat between France and Italy erupted this week after Macron accused Rome of “cynicism and irresponsibility” for refusing to let the Aquarius dock.

Italy’s new government hit back, accusing Paris of giving “hypocritical lessons” and threatening to pull out of the meeting with Macron.

Rome also summoned the French ambassador over the dispute – the second time it has done so over the migrant crisis in two months.

Macron, who has taken a tough line on migration from African countries that are not at war, said that “none of his comments were intended to offend Italy or the Italian people.”

In a further gesture of reconciliation, the French foreign ministry said it was ready to welcome migrants on board Aquarius who “meet the criteria for asylum” after they arrive in Spain.