Portugal’s new prime minister, Luís Montenegro, has promised stable government after the country’s president invited him to try to form a minority administration that could face a rough ride in a hung parliament.

Montenegro, 51, was named prime minister early on Thursday after a long-awaited count of overseas votes confirmed a narrow victory in 10 March elections for his centre-right Democratic Alliance (AD).

Overall, the AD won 80 seats, far from a majority in the 230-seat legislature, followed by the Socialists with 78 seats and the far-right Chega party, which was founded just five years ago, with 50.

“There is no internal or external reason to doubt our ability to have a stable government,” Montenegro said on Thursday after meeting the European Commission president, Ursula von der Leyen, in Brussels.

His government “has the confidence of the voters”, he said. “It also has what is required of all political players, including those now in opposition, that is a sense of responsibility.”

Montenegro, who said his government aimed to take office on 2 April, has pledged not to enter a coalition or even an informal alliance with Chega – his only route to a majority – and must now try to agree with the Socialist party (PS) a legislative programme and cabinet that the centre-left party is prepared to back in parliament.

On Tuesday the president, Marcelo Rebelo de Sousa, met the Socialists’ new leader, Pedro Nuno Santos, who promised that his party would be a “stable, strong and solid” opposition, but also that it would be a “responsible opposition” that was “open to agreements”.

The PS would not back proposals with which it did not agree, he said, but nor would it oppose “where there are common points of view”, such as on the need to boost pay for public sector workers including teachers, health professionals and police.

Chega, which emerged as potential kingmaker after campaigning on a platform calling for stricter controls on immigration and tougher measures to fight corruption, has demanded a government role in exchange for supporting an AD-led administration.

The populist party’s leader, André Ventura, said after a meeting with Rebelo de Sousa on Monday that if AD continued to reject a coalition with Chega, voters would inevitably blame the centre-right party for any political instability that ensued.

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“We are continuing to put in all our efforts … to reach an agreement that will ensure the country’s stability,” Ventura said. “If there is no government agreement, the AD will be responsible for the instability that will result.”

António Costa Pinto, a political scientist at the University of Lisbon, told Agence France-Presse that a minority administration would “not necessarily” be unstable because “none of the actors has an interest in triggering a crisis”.

Another political scientist, José Adelino Maltez, told the Diário de Notícias newspaper that “in political terms there is no crisis. Seventy per cent of the AD programme is 70% of the PS programme. There is great stability on all the essential objectives.”

However, Montenegro is already coming under heavy pressure from a small but determined group of MPs from his Social Democratic party (PSD) who argue that a stable majority government in alliance with Chega is the only responsible course.

Without it, Montenegro will be obliged to try to pass legislation on a case-by-case basis, and his government could face a survival test as early as this autumn when it tries to draw up the 2025 budget. A rejected budget could lead to a new election.