The three broke out of a maximum-security prison almost two weeks ago.
President Mauricio Macri's office initially said they had been captured north-west of Buenos Aires, but police later said two remained at large.
The latest twist is a major embarrassment to the new president, correspondents say.
The police manhunt - shown on live television - has gripped the country.
Police say the man they captured, Martin Lanatta, was caught after the car the men were travelling in rolled over in the chase in Santa Fe province, about 500km (300 miles) from the capital.
The other two escaped on foot.
Victor Schillaci and brothers Cristian and Martin Lanatta were serving life in prison for kidnapping and murdering three men allegedly connected to a drug trafficking ring.
President Macri - a conservative who replaced Cristina Fernandez de Kirchner after elections in December - had accused the previous administration of not doing enough to crack down on drug crime.
Last month the men escaped from one of the country's most secure prisons using a fake gun to threaten one of the guards.
Martin Lanatta, had leapt into the political limelight last year when he accused the presidential chief of staff, Anibal Fernandez, of complicity in the killings.
Mr Fernandez denied the accusation but it damaged his campaign last October to become the new governor of Buenos Aires province.
The candidate who won, Maria Eugenia Vidal, dismissed the intrigue and said the jail-break had been an inside job.
She sacked the head of the prison service.
A huge manhunt in Argentina netted only one of three fugitives convicted of a triple murder, officials said hours after claiming all had been caught.