"We have let the Spanish people choose between war and peace," said the statement received by the London-based newspaper Al-Quds Al-Arabi.
"They chose peace by electing the party which opposed the alliance with America in its war against Islam," said the text signed by Abu-Hafs Al-Masri/al-Qaida Brigades.
The authenticity of the statement, which followed last week's train bombings in Madrid that killed 201 people and were claimed by the same group, could not be confirmed.
"That's why the leadership has decided to halt all operations on Spanish territory against civilian targets until we know the direction taken by the new government which has promised to withdraw the Spanish army from Iraq, and that we are sure of the government's non-interference in Muslim affairs," it said.
"So we call on all the brigades which are on European territory to halt these operations."