The summons comes after Spain's chief prosecutor on Monday said he would press charges including rebellion.
Mr Puigdemont is in Belgium with several former ministers. He earlier said he was not there to seek asylum.
Carles Puigdemont triggered a crisis in Spain by holding an independence referendum in early October in the semi-autonomous region despite Madrid's opposition and the Constitutional Court declaring the vote illegal.
Spain's central government has now taken direct control of Catalonia.
Mr Puigdemont turned up in Brussels on Monday as Spanish Attorney-General José Manuel Maza called for Catalan leaders to face charges of rebellion, sedition and misuse of public funds.
The Audiencia National has now summoned the sacked Catalan officials - who are yet to be formally charged - to testify on Thursday and Friday. If they do not appear, prosecutors could order their arrest.
Meanwhile, the speaker of Catalan's dissolved parliament Carme Forcadell and other former lawmakers have been summoned to the Supreme Court because they still have parliamentary immunity.
Mr Puigdemont earlier said he would return to Spain if guaranteed a fair hearing.
Several of Mr Puigdemont's former colleagues who remain inside the country may decide to accept the summons and appear in court, reports the BBC's James Reynolds from Barcelona.
Prosecutors' arguments against the group were "serious, rational and logical", Judge Carmen Lamela said in a ruling, according to the AFP news agency.
The charge of rebellion carries a maximum 30-year jail term.
Speaking at a press conference earlier on Tuesday, Mr Puigdemont said he was not trying to escape justice by travelling to Belgium but wanted to be able to speak freely.
His comments came as Spain's constitutional court suspended the declaration of independence made by the Catalan parliament on Friday.
Mr Puigdemont also said he would accept the result of snap elections in Catalonia on 21 December, which were called by Spain's central government after it invoked Article 155 of the constitution, temporarily suspending the region's autonomy.
"I want a clear commitment from the state. Will the state respect the results that could give separatist forces a majority?" Mr Puigdemont asked reporters.
People hold a Catalan flag during a demonstration of pro and anti-Catalans in front of the Press Club in Brussels, on October 31, 2017 during a press conference of the CataloniaImage copyright AFP
Image caption Protesters from both sides turned up outside the Press Club in Brussels were Mr Puigdemont spoke
The Spanish government has previously said he is welcome to take part in the fresh polls.
In a separate development on Tuesday, Spain's Guardia Civil - a paramilitary force charged with police duties - raided the offices of the Catalan police force.
According to media reports, they searched eight offices for communications relating to the referendum on 1 October.
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