According to Puigdemont, he has enough support in parliament to be elected regional president.
But they also recognised that if they couldn't, they would pick an alternative candidate to unblock the political impasse in Catalonia, which was put under direct rule by Madrid on October 27 after a failed secession bid.
Inés Arrimadas, the leader of Ciudadnos, the main pro-Spanish party in Catalonia, accused Torra of failing to compromise.
What happens next? Regional lawmakers must vote in favor of Torra's candidacy.
Mr Torra, vice-president of the activist group Omnium Cultural - whose leader, Jordi Cuixart, has been in preventative prison since October - is the so-called "Plan D" candidate after three previous inauguration attempts were blocked by the Spanish courts.
Backing unilateral independence over the negotiated exit favoured by larger separatist parties, the CUP has previously broken ranks with the pro-independence block.
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Separatist lawmakers changed regional laws Friday to allow Catalonia's president to be sworn in without being present.
He is the fourth candidate to attempt to fill the role following a regional election in December in which pro-independence parties won a slim majority. "Our group proposes member of parliament Quim Torra to be president of the Catalan government so he can take on this responsibility in the next few days and so that a government can be formed immediately", Puigdemont said.
The Spanish government said Mr Torra's speech was "confrontational".
There he specialised in reviving texts by Catalan journalists from the civil war and Francisco Franco's dictatorship, which severely repressed Catalonia among other regions.
Puigdemont is now in Germany after being detained there in March on a European arrest warrant against him issued by Spain.
But a German court rejected extraditing him on that charge, judging that rebellion implies violence, and ruling that Puigdemont was not personally involved in violent acts during the referendum.