Spain has vowed to crush the Basque separatist group Eta after the arrest on Sunday of an alleged leader in raids by police in France.
Albizu and Iparraguirre had been on the run for more than 10 years
Spanish Interior Minister Jose Antonio Alonso called the arrest of Mikel Albizu and 20 others "an extremely hard blow to the terrorist gang".
But he said Spanish security forces cannot let down their guard.
Officials said Sunday's operation was possibly the most significant blow against Eta in years.
"It is an extremely severe blow to the terrorist group and a
blow of which we must feel extraordinarily satisfied," Mr Alonso told Spanish TV.
"Eta is now more weakened and is in very bad shape but... we must not ease up for even a minute in the fight against Eta's terrorism."
The weapons and explosives seized in Sunday's raids showed Eta was still very capable of attacking, he said.
On the run
Mr Albizu Iriarte, known as Antza, and his partner, Maria Soledad Iparraguirre, know as Anboto, were among at least 20 people detained in a swoop in south-western France.
Mr Albizu is thought to be one of the most senior political figures in Eta.
Ms Iparraguirre is one of the group's leading female figures.
The couple, both aged 43, had been on the run from Spanish justice for more than 10 years. They were arrested near Pau in south-western France.
They were with their child when they were arrested,
according to police, the Associated Press reports.
They had false papers and refused to answer questions, but were identified by police and, Spain said, by their fingerprints.
Their arrests were part of a series made in border villages along the French border where Eta militants have long sought refuge.
Mr Alonso says the raids are hugely important and an example of outstanding collaboration between the two countries.
Improved French and Spanish ties since the 11 September attacks in the Unied States have led to several high-profile Eta arrests, the BBC's Katya Adler in Madrid says.
The armed group has been fighting for more than 30 years for an independent Basque state.