"We have to try somehow to calm things down, relax the mood, and resume relations," Foreign Minister Jose Manuel Garcia Margallo said in an interview with Spanish public broadcaster TVE.
Bolivia reacted furiously after Morales, flying home from Moscow on Tuesday, had to land in Vienna, accusing several European nations of denying his jet overfly rights.
Spain's foreign minister denied, however, that his country closed its airspace to the Bolivian leader's plane, which resumed its journey on Wednesday and refuelled in Las Palmas on the Spanish archipelago of the Canary Islands.
"What Spain said was that in no case was it going to restrict its airspace and that it would keep its authorization in force so the plane could land and refuel in Las Palmas," Margallo said.
Bolivia accused France, Portugal, Italy and Spain of denying flyover rights because they suspected the plane was carrying Snowden, who is seeking to avoid US espionage charges after leaking embarrassing details of a vast US phone and Internet surveillance programme.
"They told us he was in the plane," said Garcia Margallo during his RTVE interview on Friday.
Asked whether Spain had been contacted by US authorities, or whether they had made contact, the foreign minister said: "That remains secret."
"European countries reacted the way they did because the information they gave us was that he (Snowdon) was on board," he added.
"We evaluated the risk (that Snowden was on the plane) but once I have a written guarantee that he isn't, I believe in the word of an ally, which Bolivia is."
The 30-year-old intelligence leaker is still believed to be holed up at a Moscow airport looking for a country that will give him safe haven.
Bolivia is one of 21 countries Snowden has asked for asylum. Morales said earlier this week that his country would be willing to study the request.
Spain had earlier said that Snowden could not apply for asylum in Spain because he was not on national soil.
In related news, Bolivia's Latin American allies have also responded with outrage to the diversion of Morales' flight to Vienna.
Ecuador said Spain had told its ambassador in Austria to board Morales’ plane in Vienna in bid to see if Snowden was on board, Spanish daily El País reported on Friday.
The newspaper also quoted Venezuelan President Nicolás Maduro as saying: “Who does that prime minister, Rajoy, think he is? He thinks South Americans are still his slaves?”
Maduro also said he would reconsider his country’s relations with the “vile” ruling Popular Party government, but “not with the people of Spain", news agency EFE reported.