The 35-year-old was called up by Vicente del Bosque for the friendly matches with Italy and Romania, five and a half years on from his first and only senior appearance in a Euro 2012 qualifier with Lithuania.
Having fired in 31 goals in all competitions for Athletic Bilbao this season, Aduriz is now hoping to replicate that form for the national team and give himself the best chance of going to Euro 2016.
"I've felt very welcome and wanted here, and I'm very grateful to be here," he told the media on Monday. "I've always tried to play the best I can for my club and I knew it was going to be difficult for me to get the call.
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"I always feel overwhelmed in these situations but that's part of football. The press is the link between players and fans and so it's normal that people were interested in my situation.
"It's not very usual for someone to get a call-up at my age, that's why I feel so privileged and happy to be here. Age is just a number. What it is important is desire, and I have that.
"I'll try to give everything I can and do the same thing I do at Athletic. Whether or not I go to the Euros depends on the boss.
"Spain has incredible players, they are at an amazing level. It must be amazing to play alongside them."
Spain face Italy in Udine on Thursday before taking on Romania three days later.