His plan is to continue working from the Belgian town of Waterloo, the secretary general of Puigdemont's Together for Catalonia party (Junts per Catalunya, or Junts), Jordi Turull, told Catalan radio station RAC1.
Puigdemont had been in Barcelona since Tuesday evening, he said.
After giving a brief speech, Puigdemont managed to flee despite a large contingent of police seeking to arrest him on Thursday.
Earlier, Puigdemont's lawyer said he was "outside the Spanish state".
Lawyer Gonzalo Boye did not state whether Puigdemont had returned to Belgium, where he has spent most of his almost seven-year exile.
Puigdemont will address the public in the near future, Boye said.
Puigdemont sought to lead Catalonia to independence in 2017 with a referendum that was declared illegal.
He then fled the country hidden in a car and spent most of his time in exile in Belgium.
He was later also based in southern France.
The Catalan police, who were supposed to arrest Puigdemont, were caught off guard as they did not expect him to disappear right after his speech, they said at a press conference.
Catalan police have opened an investigation into how Carles Puigdemont escaped and avoided arrest. (EPA PHOTO)
Puigdemont had said in advance that he wanted to be present for the election of pro-Spanish Socialist Salvador Illa as the new leader in the region's parliament.
However, after speaking, Puigdemont escaped in a white car, reports said.
Two policemen were later arrested on suspicion of helping him flee.
The leadership of the Catalan police admitted a failure in the arrest of Puigdemont in Barcelona.
At the same time, Chief Commissioner Eduard Sallent appealed for understanding for the way the security forces acted.
Sallent said that the most important objectives on Thursday were to maintain public order and to secure the election of a new head of the Catalan government in the parliament in Barcelona, tasks that had been fulfilled.
He said why the arrest of Puigdemont was not successful still needed to be analysed in more detail.
Sallent confirmed that the police had assumed in their planning that Puigdemont would go to parliament on Thursday, as he had repeatedly announced, and why officers were stationed there.
"This seemed to us to be the most favourable place for an arrest," said Sallent.
But after giving his four-minute speech, Puigdemont was driven off in a waiting vehicle behind the stage.
"It all happened very quickly and our officers were unable to intervene because of a wall of people," said Sallent.
El Parlament de Catalunya ha convocat a tots els diputats al debat d'investidura del pròxim president de la Generalitat. Jo hi he de ser i hi vull ser. Per això he emprès el viatge de retorn des de l'exili. — krls.eth / Carles Puigdemont (@KRLS) pic.twitter.com/jcO5MA8czXAugust 7, 2024
During his brief appearance, Puigdemont was also accompanied by representatives of the state, parliament and many supporters, further hindrances to an intervention, he said.
Also, two police officers helped Puigdemont, who were later detained.
Catalonia's interior minister, Joan Ignasi Elena, strongly criticised the Spanish judiciary, calling it an "abnormal situation" in which a judge refuses to apply an amnesty law to the people for whom it was made, in comments to the press conference.
Spain has an amnesty for separatists, but there is still an arrest warrant for Puigdemont, accused by investigating judge Pablo Llarena of embezzlement in 2017, an offence exempt from the amnesty.
Investigating judge Llarena is now demanding an explanation from the police as to how Puigdemont managed to escape.
Earlier, Puigdemont said he is "healthy, safe and above all free," Lluís Llach, a Catalan singer-songwriter and head of the separatist civic movement Catalan National Assembly (ANC), said in a post on the social media platform X.
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