Spain has been gripped by a constitutional crisis since a referendum, organised by Mr Puigdemont's separatist government, was held on 1 October in defiance of a constitutional court ruling that had declared it illegal.
The Catalan government said that of the 43% of potential voters who took part, 90% were in favour of independence.
After the regional parliament declared independence, Spain's took direct control and sacked the government, including Mr Puigdemont.
On Monday, Spain's chief prosecutor said the Catalan leaders were accused of rebellion - which carries a maximum 30 year jail term - as well as sedition and misuse of funds.
The leaders are yet to be formally charged but are due to testify at the Audiencia National (National Court) on Thursday and Friday.
The court summons also gave them three days to pay a deposit of €6.2m ($7.2m) to cover potential liabilities.
Both Mr Puigdemont and his lawyer denied at a news conference on Tuesday that he had travelled to Belgium to seek asylum.
He said he was there "for safety purposes" and wanted to be able to speak freely.
Joaquim Forn and Dolors Bassa, the deposed Catalan interior and labour ministers who travelled with the former Catalan president to Belgium, returned to Barcelona on Tuesday night.
They were greeted by chants of "off to prison" by some crowds that had gathered at Barcelona international airport, according to media reports.
Mr Puigdemont previously said he would return to Spain if he and his colleagues received guarantees of a fair trial from the Spanish government.