Legislators in the autonomous community, where Spain's ruling Socialists won control earlier this year, also voted to ask organisers of the Tour of Spain (La Vuelta) to bring the cycling race back for the first time in 31 years.
The authorities have been reluctant to stage major sporting events in the Basque Country in part due to the activities of ETA, the guerrilla group which has killed more than 800 people in its campaign for independence.
Spain's last match there was a European Championship qualifier against Turkey played at Athletic Bilbao's San Mames stadium on May 31, 1967, and the Vuelta has not passed through since 1978.
Gorka Maneiro, a representative from the Progress and Democracy Union who proposed the two motions, said the move was designed to inject a "dose of normality."
"The Spanish soccer team has become a global icon in recent years," Maneiro said. "Their talent suggests they will be well received at any stadium, including any of the Basque ones."
The Socialist Party won control of the community earlier this year after ousting the Basque Nationalist Party (PNV), which had been in power since 1980.
Socialist leader Patxi Lopez is the first head of the Basque Country who unequivocally backs unity with the rest of Spain since the region was granted wide autonomy in 1979 after the end of the Franco dictatorship.
Most Basques favour some sort of independence from Spain, although only a minority sympathise with violent separatists, polls have shown.
