"ETA maintains its 'decision to continue its fight' and its disposition to achieve a resolution 'through dialogue'," Gara said, quoting an ETA communique in the Basque language.
The group, listed as terrorists by the European Union and the United States, has used Gara in the past to publish statements.
The Socialist party had no immediate comment.
"We're reading the statement and there will certainly be a reaction later," a spokesperson said.
ETA has reportedly killed about 840 people in a four-decade struggle for an independent Basque homeland in north-eastern Spain and south-western France.
Last year, it carried out three killings - its lowest tally since 1973, except for a 14-month ceasefire in 1999.
Mainstream Basque nationalists have urged Madrid for years to follow Britain's example in opening a dialogue with Sinn Fein, the political ally of Irish Republican Army (IRA) guerrillas fighting British rule in Northern Ireland.
No easy solution
Gara quoted ETA as urging Socialist leader Jose Luis Rodriguez Zapatero to adopt "strong and bold measures for the Basque country" in a statement dated 16 March - two days after his election win - but only published on Sunday.
ETA said it was possible to reach peace "through reason and common sense", but acknowledged "it will not be easy".
Zapatero says there will be no
let-up in the crackdown on ETA
Zapatero has said there will be no let-up in the crackdown on ETA.
"What I am thinking, planning and working towards is to finish off terrorism and ETA is not going to get a minute's rest," he said on 17 March.
The outgoing government of Prime Minister Jose Maria Aznar initially blamed ETA for the 11 March train bombings in Madrid that killed 202 people, but suspicion has now fallen squarely on other groupings.
Aznar's office had no immediate comment on Sunday.