Ousted Catalan president Carles Puigdemont has demanded Madrid reinstate his regional government, which was deposed after an independence referendum that Spanish courts judged illegal, as part of a political settlement.

"As president, I demand the Spanish government and those who support it ... restore all they have expropriated from the Catalans without their say-so," Mr Puigdemont said from Brussels as he called on the government to "negotiate politically".

Mr Puigdemont's administration followed up an October referendum by declaring independence, but the government promptly sacked him and his team and, facing arrest, he fled to Belgium while colleagues were arrested and jailed.

He campaigned for the region's December snap election from his Brussels base after a Spanish court charged him with rebellion, sedition and misuse of public funds.

The election failed to resolve Spain's biggest political crisis in decades with pro-independence parties taking 70 of 135 seats in the Catalan parliament but not managing to gain a majority of the popular vote.

In a seven-minute recorded message, Mr Puigdemont insisted he was still Catalonia's "legitimate" leader and that the electorate had shown themselves to be "democratically mature, winning the right to constitute a republic of free men and women". 

After the divisive regional elections, how the independence camp intends to rule remains a mystery, with other secessionist leaders, including Mr Puigdemont's former deputy, Oriol Junqueras, behind bars pending trial.

"The ballot box has spoken," said Mr Puigdemont, who said he hoped the election outcome could kick start moves towards "dialogue and negotiation."

Spanish Prime Minister Mariano Rajoy on Friday denounced as "absurd" any idea that Mr Puigdemont could govern from abroad and Ines Arrimadas, regional head of the anti-independence Cuidadanos party, agreed.

"Mr Puigdemont believes he can be president of the Generalitat [regional executive] via internet and Whatsapp," Mr Arrimadas said.