Since late 2016, Mr. Rajoy has led a minority government, but his Popular Party has a majority of the seats in the Senate, the upper chamber of the Spanish Parliament and the one in charge of approving Article 155.

Mr. Rajoy is therefore already guaranteed to get the Senate’s approval. In recent days, however, he has pushed for the Socialists and other parties to back his use of Article 155, as the best way to share political responsibility and to build a common front to defend Spain’s Constitution and national sovereignty.

Ciudadanos, a party that was founded to oppose Catalan secessionism, is Mr. Rajoy’s main parliamentary ally. It has been pushing for Article 155 since the crisis escalated last month.

The Socialists have also said they backed Article 155, but they have been ambiguous about how it should be used. José Luis Ábalos, a senior Socialist official, said on Thursday that the party would support Mr. Rajoy — as long as the prime minister made “very very limited” and short use of Article 155, and also somehow kept “self-government” in Catalonia.

Among Spain’s main parties, only the far-left Podemos is against using Article 155, which it considers to be a disproportionate response. Pablo Iglesias, the leader of Podemos, wants a Spanish referendum over Catalonia’s future.

Will there be new elections in Catalonia?

Almost certainly yes. Mr. Rajoy said that his goal was to arrange new Catalan elections within six months, so as to lift the measures taken under Article 155 as soon as possible.

But it’s not clear who will convene them — and whether they will help end the conflict.

Mr. Rajoy’s government and other party leaders in Madrid have been urging Mr. Puigdemont to hold new elections rather than push ahead with his secessionist plan — so far to no avail.