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 traveling 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.
Security Minister Patricia Bullrich announced yesterday a national security emergency in Argentina, part of the government’s plan to combat organised crime.
“The concept of the [security] emergency is in a broad sense,” Bullrich told the press after the meeting, although she clarified that drug trafficking and large-scale crime would be the main priorities.
“It has to do with organised, complex crime and looking after the public. But there are also longer term issues, such as seeking agreements in education, that are not specifically related to the emergency,” added Bullrich.
The meeting included security ministers from all the provinces throughout the country, as well as the heads of various police and security forces including the federal, metropolitan, navy, and border apparatuses in an attempt to “coordinate mechanisms of action together.”
Bullrich outlined the creation of a new border secretariat that would work in “provinces that have problems with drug trafficking.” She also proposed various goals for the future of policing in Argentina.