Spain's Socialist government had planned to move the remains on Monday from the opulent mausoleum near Madrid to a more discreet state-run pantheon but the plans have been fiercely resisted for nearly a year by Franco's heirs.
The court said in a statement it had decided unanimously to suspend the exhumation to avoid “harm” that could be caused if it was ultimately found that his remains should not have been moved.
Prime Minister Pedro Sanchez's government has made transferring Franco's remains a priority since he took office in June 2018, arguing the country could not “continue to glorify” the dictator.
The government said in a statement it was “convinced” that the court will ultimately reject the family's appeal when it gives a final verdict “in the coming months”.
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Franco, who ruled with an iron fist from the end of the 1936-39 civil war until his death in 1975, is buried in an imposing basilica carved into a mountain at the Valley of the Fallen, 50 kilometres (30 miles) outside Madrid.
A 150-metre (500-feet) cross towers over the site.
Built by Franco's regime between 1940 and 1959 — in part by the forced labour of some 20,000 political prisoners — the monument holds the remains of 37,000 dead from both sides of the war, which was triggered by Franco's rebellion against an elected Republican government.
It was long used for tributes to the dictator on the anniversary of his death, but that was stopped by a 2007 law.
Franco, whose Nationalist forces defeated the Republicans, dedicated the site to “all the fallen” of the conflict in an attempt at reconciliation but critics say it is unacceptable to give such ostentatious recognition to a
Critics compare the situation with neighbouring Portugal, where late dictator Antonio de Oliveira Salazar is buried in a municipal cemetery, or Italy, where former fascist leader Benito Mussolini lies in a family crypt.
Many on the left are repulsed by the existence of the Valley of the Fallen, comparing it to a monument glorifying Hitler. Others, often on the right, insist it is just a piece of history that has had its meaning twisted by critics.
The government planned to move Franco's remains from the Valley of the Fallen to be reburied next to his wife in the family tomb at Mingorrubio El Pardo, a state cemetery where various political figures are buried. The ceremony ws to take place without media coverage.
But Franco's closest living relatives, his grandchildren, had asked that the Supreme Court suspend the exhumation until it reaches a final ruling on the case, arguing it should not take place until all of the legal channels have been explored.
Luis Felipe Utrera-Molina, a lawyer for the family and the son of a minister in the dictator's government, welcomed the court ruling, telling Spanish public television that it showed that his client's arguments were
“worthy of consideration”.
If the exhumation could not be stopped, Franco's heirs had wanted his remains to be moved to the Almudena Cathedral in Madrid where his daughter is buried.
But the government feared the central location could become a pilgrimage site for Franco supporters and successfully lobbied the Vatican to reject this option.
Less than half of all Spaniards, 48.9 percent, supported the government's plan to exhume Franco's remains, in a poll published in January by online newspaper El Español.
About a third, 30.6 percent, opposed it.