While in Bilbao, Mr Adams hopes to make a prison visit to his old friend and political ally Karmelo Landa, a member of HB's national executive who was jailed with the rest of the party's leadership last December for collaborating with terrorism.
Mr Landa used to be HB's international secretary and attended Sinn Fein events and conferences over the past two years as the Irish peace process took shape.
Mr Adams will also meet representatives of the broad Basque front whose "Irish Forum" signed a pact three weeks ago that called for the opening of talks with armed nationalists even before they agreed a ceasefire.
They want him to take a copy of their agreement - the Pact of Estella (Lizarra in Basque) - to President Bill Clinton, whom Mr Adams is due to visit in the United States this week.
The conservative government of Jose Maria Aznar, after a sceptical initial response to Eta's truce, has thawed after sounding out other main political parties in Madrid, where a bipartisan policy appears to be shaping up.
Mr Aznar said on Friday evening he was ready to take steps towards meeting long-standing Basque grievances if Eta demonstrated that the truce would be permanent.
This is taken to mean not that Eta must immediately hand over its arms, but should renounce violence and accept the results of Basque regional elections on 25 October as a framework for negotiating peace.
Mr Aznar promises in return a more flexible policy towards Eta prisoners, bringing them nearer home to Basque prisons, allowing those who have served the bulk of their sentence a more open regime of partial release and, in some cases, granting pardons.
More than 530 Eta prisoners are dispersed throughout Spain, mostly far from the Basque Country, some in the Canary Islands and Spain's Moroccan enclaves of Ceuta and Melilla.
A question remains over the timing of all this. The government wants to take no action until after the 25 October poll, but Basque nationalists, both radial and conservative, are pressing Mr Aznar to keep up the momentum and show a goodwill gesture within the next three weeks.
Basque nationalist parties are expected to make electoral gains at the expense of Madrid's ruling conservative Popular Party, and Mr Aznar may be tempted to make a popular gesture ahead of polling day, such as bringing home a dozen or so prisoners suffering health or family problems.Reuse content