"The Russian embassy in Madrid has just told us that it is withdrawing its demand for permission to stop over for the boats, which means that the stop-overs have been cancelled," Spain's Foreign Ministry said in a statement.
“We confirm that the request has been withdrawn,” an official of the Russian Embassy in Spain told RIA Novosti on Wednesday.
Spain had faced pressure from its Nato allies to refuse permission for Russian warships headed for the Syrian coast to refuel at its north African enclave on the Strait of Gibraltar.
The Russian flotilla - led by the aircraft carrier Admiral Kuznetsov - had been expected to arrive in Ceuta on Wednesday en route to the eastern Mediterranean to boost its naval forces in the area.
Russia has been staging a bombing campaign in Syria for the past year in support of President Bashar al-Assad and has deployed a naval contingent to back up its operation.
Nato Secretary-General Jens Stoltenberg expressed concern that the flotilla could take part in Syria air strikes.
"It's a decision which has been taken by individual allies whether they provide fuelling and supplies to Russian ships," he told reporters in Brussels.
"But this time I have conveyed a very clear message that we are concerned about the potential of this carrier group to increase attacks in Aleppo," he added.
"All allies are aware of our concerns, they share our concerns about Russian airstrikes against Aleppo."
Britain also weighed in. A British government spokesman said London "has previously expressed concerns to the Spanish government about its hospitality to the Russian navy when we have concerns about Russia's military activity."
Guy Verhofstadt, former Belgian premier and liberal leader in the EU parliament, said in a Twitter message "it is scandalous that Spain, a member of NATO and the EU, is today allowing the Russian Kuznetsov fleet to refuel and receive technical assistance on Spanish territory."
He recalled that just last week the Spanish government signed a European Council statement accusing Russia of war crimes against civilians in Syria.
Spain, a NATO member, regularly allows Russian war ships to stop in Ceuta, which faces the British territory of Gibraltar on Spain's southern tip.
At least 57 Russian navy ships have stopped in Ceuta between 2011 - when Moscow started to regularly use the port facilities there - and August 2015, according to conservative US think tank Heritage Foundation.
The foundation blasted Spain for allowing Russia to use the port even after Russia invaded and annexed Crimea in March 2014.
It said Greece, another NATO member, as well as Malta, which is part of the EU but not NATO, also allow Russian navy ships to use their ports.
The Russian flotilla is being followed by the Spanish navy as it makes its way from the Atlantic to the Mediterranean, the Spanish defence ministry said.