By Sergio Goncalves, Catarina Demony and David Latona

LISBON (Reuters) -The leader of Portugal's centre-left Socialists conceded defeat in Sunday's parliamentary election after his party came in second to its centre-right rivals by a razor-thin margin, while the far right's share of the vote grew significantly.

With 99% of ballots counted, the Socialist Party (PS) trailed by only 438 votes, virtualy tied at 28.7% with the centre-right Democratic Alliance (AD), though the tally from voting abroad was still pending.

But a separate conservative outfit from the region of Madeira elected three lawmakers, boosting the AD's cause.

The AD and its Madeira allies won a total of at least 77 seats in the 230-seat parliament, ahead of the PS's 74. Far-right Chega came in third with 46. With 11 seats yet to be attributed after the final count, the combined right clearly dominated the new legislature.

PS leader Pedro Nuno Santos' concession speech erased all doubts about the winner when he congratulated the AD on its victory despite his party's late surge in the tally.

The PS, in power since late 2015, had trailed the AD in most opinion polls since Socialist Prime Minister Antonio Costa resigned in November amid a corruption investigation.

Santos said his party would now lead the opposition, which could not be left in the hands of Chega.

The populist party came third with over 18% of the vote, almost tripling its 2022 election result, likely giving the combined right a parliamentary majority, although the moderate AD has so far refused to negotiate with the populists.

Chega leader Andre Ventura told reporters Sunday's vote "clearly showed that the Portuguese want a government of the AD with Chega".

It campaigned on an anti-establishment message, vowing to sweep away corruption and expressing hostility to what it sees as "excessive" immigration.

The PS and the Social Democratic Party (PSD), which helms the newly created AD, have alternated in power since the end of a fascist dictatorship five decades ago.

At the AD election night party, supporter Paula Madeiro said there was "no doubt that instability will be constant".

Alexandra Ferreira, a 21-year-old law student and member of the Socialist Party, said she was "very sad" with the results because of the far-right's growth. She said it showed that "we have a society with no memory", in reference to the dictatorship that ended in 1974.

Sunday's ballot was triggered by Socialist Prime Minister Antonio Costa's resignation amid a graft investigation four months ago.

Issues dominating the campaign in western Europe's poorest country include a crippling housing crisis, low wages, sagging healthcare and corruption, seen by many as endemic to the mainstream parties. 

(Reporting by Sergio Goncalves and Catarina Demony Writing by Andrei Khalip and David LatonaEditing by Frances Kerry, Christina Fincher, Giles Elgood, Stephen Coates)