Video report by ITV News Correspondent Emma Murphy
Carles Puigdemont and Spanish prime minister Mariano Rajoy are willing to engage in new talks to discuss Catalonia's future.
Mr Rajoy and ex-Catalan leader Mr Puigdemont both expressed their hope for a "new era based on dialogue" between Spain and the region.
It comes after secessionist parties in Catalonia have regained their majority in the regional parliament following an election.
The victory, albeit by a slim margin, will likely give fresh momentum to the push to break away from Spain.
It is also a blow to Madrid, which dissolved the Catalan parliament after separatists held a referendum on October 1, declaring the region independent.
Mr Rajoy called the election in a bid to stop the movement to break away from Spain.
But the result favoured fugitive leader Mr Puigdemont, who was forced to campaign from Belgium after fleeing Spain to avoid a judicial probe that could lead to jail time on charges of sedition should he return.
Mr Puigdemont got the most votes of any separatist candidate.
"The Spanish state has been defeated," the 54-year-old said in a televised address.
"Mariano Rajoy has received a slap in the face from Catalonia."
Following the result, Mr Rajoy said that the election's outcome, which also gave the pro-Spain Ciutadans (Citizens) party the most votes, showed a diversity of views in Catalonia that compel the new government to abide by the law.
He indicated he would talk with the region's new leaders as long as they didn't violate Spain's constitution.
Catalonia's earlier referendum was dubbed unconstitutional by Madrid.