An opinion poll released to coincide with Tuesday's anniversary found that a third of Spaniards thought that right-wing army officers were justified in their their revolt that led to war 70 years ago.
But at the same time, 51% of people believed the uprising by Franco's nationalist forces had "no justification", according to the poll commissioned by El Mundo, a Spanish newspaper.
The resulting conflict between Franco's right-wing followers and left-wing republicans killed between 300,000 and 1 million people. Many of the dead were civilians killed in the world's first large-scale air-raids and in the war's countless massacres.
The war ended in 1939 when the right-wing leader General Francisco Franco defeated his leftist opponents and established himself as ruler.
Since his death in 1975 successive Spanish governments have tried to efface his memory.
But despite this, Tuesday's poll found that just over half the supporters of the Popular Party, the main present-day conservative opposition party, believe that Franco was right to topple Spain's democratically elected left-wing government in 1936.
In addition, 42.6% of practising Catholics said they shared that view - but so did almost one in five Socialist voters.
Franco portrayed himself as a defender of Spanish values against Communism and received help from Hitler's Germany. Many of his left-wing opponents were supported by the Soviet Union.
Despite Spain's enduring divisions, most Spanish believe that the country should face up to its past and honour all the war's victims equally.
One poll conducted by El Pais newspaper found that 64.5% of all Spaniards favoured a "rehabilitation of all victims."
In recent years, left-wing parties have campaigned for Franco's victims to be given greater recognition.
Streets associated with Franco have already been renamed and monuments to his regime have been dismantled.
During the war, about 150,000 Republican supporters, 60,000 right-wing nationalists and 50,000 left-wing sympathisers were executed.
The Socialist government of prime minister Jose Luis Rodriguez Zapatero, whose grandfather was executed by pro-Franco forces, will shortly approve a new "law of historic memory" to compensate Civil War and Franco-era victims.
But the legislation's passage has been frequently delayed, and many fear that the atrocities committed during the period will continue to be glossed over.