The move is in recognition of the events in Catalonia, where the regional government was deposed after the unilateral declaration of independence.
Protests have been held against the detention of the region's ex-leaders.
Eight politicians are being held in an investigation by Madrid authorities into alleged rebellion and sedition linked to the declaration of independence that followed a banned referendum.
"We've created a committee in parliament to explore the possibility of amending the constitution to be able to accommodate better the aspirations of some of the Catalan people," Mr Dastis said.
"[But] a decision will have to be taken by all Spaniards."
The Spanish government imposed direct rule over Catalonia after its declaration of independence and announced new elections for 21 December.
In a speech to parliament, Prime Minister Mariano Rajoy called for a big turnout in the vote so that Spain could get over the crisis.
He said sacked Catalan President Carles Puigdemont did not have the power to unilaterally declare the region's independence from Spain.
"A regional leader cannot say the constitution doesn't rule in his territory. A regional leader cannot invent a parallel legal framework."
On Wednesday, protesters blocked all major roads and some railway stations across Catalonia against the detention of the separatist leaders. Minor scuffles were reported when police moved in to remove protesters.
But a call for a general strike was not backed by the region's major unions, and shops and businesses appeared to be open as normal.
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