Catalonia’s pro-independence coalition splintered on Saturday over a proposal by Carles Puigdemont, the former leader of the restive Spanish region, to select his replacement from his own party while he remained in Belgium to avoid prosecution in Spain.

The political committee of the Popular Unity Candidacy — a far-left party known by its Catalan acronym, CUP — announced that its lawmakers would abstain from voting if two larger separatist parties presented Jordi Sanchez as candidate to lead Catalonia — as Mr. Puigdemont had proposed on Thursday, when he agreed to give up his campaign to be reappointed.

CUP has only four lawmakers among the 135 in the Catalan Parliament, but its backing is essential for the separatist coalition to keep the thin majority of 72 seats that it won in December, after Prime Minister Mariano Rajoy of Spain called a snap election in the region.

One of the CUP lawmakers, Vidal Aragonés, on Saturday portrayed his party’s decision not as an attack on Mr. Sanchez himself, but as a way of criticizing other separatist parties for focusing on who should lead the pro-independence movement instead of agreeing on policies and a plan “to materialize the republic” of Catalonia, independent from Spain.