Responding to an initial deadline set by the central government, Carles Puigdemont called for talks with Prime Minister Mariano Rajoy "as soon as possible" as Spain struggles with its worst political crisis in decades.
But Puidgemont stopped short of giving a definitive "yes or no" as demanded by Madrid, and Spain gave him until Thursday morning to clarify.
Anything less than a full climb-down by Thursday's 0800 GMT deadline is likely to prompt moves by Madrid to impose direct control over the semi-autonomous region -- the so-called "nuclear option."
"All we are asking for is clarity."
The crisis has showed no signs of abating since a banned independence referendum on October 1, when a violent police crackdown on Catalan voters shocked the world.
Puigdemont declared last week that he was ready for Catalonia to "become an independent state" after the referendum produced a 90 percent 'Yes' vote, although turnout was only 43 percent and many of those who back unity with Spain stayed at home.
Unideco, the parent company of winemaker Codirniu Raventos which markets itself as Spain's oldest family business, on Monday became the latest of hundreds of companies to move their headquarters out of wealthy Catalonia in a bid to minimise the instability.
Adding to the tensions, Catalan police chief Josep Lluis Trapero appeared in court accused of failing to stop the referendum going ahead, with Spanish prosecutors demanding he be remanded in custody.
Puigdemont wrote in his letter to Rajoy that "for the next two months, our main objective is to bring you to dialogue."
Rajoy said in a written response that it was "absolutely necessary" that Catalonia clarify its position.
"I hope that in the hours that remain until the second deadline... you reply with all the clarity which citizens demand and the law requires," Rajoy said, calling on the Catalan separatists to "return to legality".
Catalonia has its own language and distinct culture but is deeply divided over independence.
Separatists argue the northeastern region pays more in taxes than it gets back and that breaking away would allow it to prosper, but those who back unity say a split would spell economic and political disaster.
Though it represents about a fifth of Spanish gross domestic product, Catalonia is deeply indebted to Madrid and cannot borrow internationally.
Madrid says the growing uncertainty imperils Spain's recovery from the financial crisis.
Puigdemont, a 54-year-old former journalist, is under intense pressure from Madrid and world leaders to back off.
Barcelona Mayor Ada Colau urged him to abandon a unilateral independence bid, saying the uncertainty was "bad for everybody".
"Before reaching a definitive solution, what we can do is bring about a stable dialogue -- and for that, it will be necessary to give up a unilateral independence declaration once and for all," she told La Sexta television.
They have threatened mass strikes and protests in the event of a climb-down.
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