Mexican President Claudia Sheinbaum has said there was "no diplomatic crisis" with Spain after years of frosty relations over the conquest of the North American nation.

"There is no diplomatic crisis. There never has been. What is very important is that we recognise the strength of our country's indigenous peoples," she said as she arrived at a summit of left-leaning leaders in Barcelona on Saturday.

Spain's colonisation of Mexico has become a thorny issue in recent years, prompting calls for an apology and an apparent diplomatic snub.

The summit, which seeks to address a rise in illiberalism, comes as far-right leaders met in Italy for a rally against immigration and EU bureaucracy.

Sheinbaum's comments came moments before she met the Barcelona summit's co-chair, Spanish Prime Minister Pedro Sánchez, who did not comment on the state of his nation's relations with Mexico.

However, Spain's economy minister was quoted by news agency Reuters as saying that Sheinbaum's presence was "a very important and positive sign of a rapprochement between the two countries".

Her visit is the first by a Mexican president in eight years.

Relations between Spain and Mexico deteriorated in 2019 when Sheinbaum's predecessor, Andrés Manuel López Obrador, demanded that Spain apologise for human rights violations during its conquest.

Spanish conquistadors killed thousands through fighting and disease as they dismantled the Aztec empire in the 16th Century.

When López Obrador's request went unanswered, Sheinbaum took the unusual decision not to invite Spain's King Felipe VI to her inauguration in 2024. Spain then refused to send any Spanish representative.

Recently, though, there have signs that relations had begun to thaw.

King Felipe said in March that there had been "a lot of abuse" during the conquest of the territory that would become Mexico.

"There are things that, when we study them, with our present-day criteria, our values, obviously cannot make us feel proud," he had said while visiting an exhibition on indigenous Mexican women in Madrid.

King Felipe's words marked the first time a Spanish monarch had publicly acknowledged abuses during the country's colonial era.

It then emerged that, a month prior, Sheinbaum had invited him to the upcoming Fifa World Cup.

She said that the sporting event - being hosted jointly with the US and Canada - would provide "a timely opportunity to evoke the depth and unique character of the ties between Mexico and Spain", according to the Spanish royal palace.

Spain's Foreign Minister José Manuel Albares won plaudits from Sheinbaum last October when he said there had been "pain and injustice" in the countries' shared history.

Saturday's summit in Spain was the fourth meeting of the In Defence of Democracy initiative, which aims to counter extremism and illiberalism.

"Democracy cannot be taken for granted," Sánchez said.

"We are witnessing attacks on the multilateral system, one attempt after another to challenge the rules of international law, and a dangerous normalisation of the use of force."

His co-chair, Brazilian President Luiz Inácio Lula da Silva, said the UN Security Council was not working and that its five permanent members - the US, China, Russia, France and the UK - all of whom hold veto power, had become "lords of war".

"No president of any country in the world, however powerful, has the right to keep imposing rules on other countries," Lula said.

The leaders of Brazil, Mexico and Spain later issued a joint statement saying they had agreed to increase aid deliveries to Cuba, which they described as undergoing a "humanitarian crisis".

The Caribbean island nation has recently been experiencing a series of nationwide blackouts as an informal US oil blockade has exacerbated an existing fuel shortage.

Meanwhile, in Milan, thousands of supporters of the Patriots for Europe party, a right-wing grouping in the European Parliament, gathered for a rally.

The party's leader, Jordan Bardella, who is also the head of France's far-right Rassemblement National (RN), took part alongside the event's organiser, Italy's Deputy Prime Minister Matteo Salvini, and Geert Wilders, who leads the Dutch far-right PVV party.

Bardella said immigration and the "ever-increasing regulations imposed by the European Commission and the European Union on European industry and on the economies of the eurozone" would be among the issues leaders discussed.

"In Europe, the Alliance of Patriots is the only true adversary for the Brussels bureaucrats who serve a few businessmen and warmongers," Salvini told the crowd.

Hungary's outgoing leader Viktor Orbán, whose Fidesz party is also a member of the Patriots for Europe, was not present at the rally. He was ousted last weekend in the country's general election by Péter Magyar, a former Orbán ally.