BEIRUT — Lebanon’s prime minister resigned Friday due to government infighting that threatens to leave a void in the state’s highest ranks at a time of rising tensions and sporadic violence inflamed by the civil war in neighboring Syria.

Najib Mikati stepped down to protest the Parliament’s ­inability to agree on a law to govern elections set for later this year, as well as for the Cabinet’s refusal to extend the ­tenure of the country’s police chief, who is about to retire.

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Underpinning the political crisis are Lebanon’s hugely ­sectarian politics and the fact that the country’s two largest political blocs support opposite sides in Syria’s civil war.

Lebanon and Syria share a complex network of political and sectarian ties, and many fear that violence in Syria will spread to Lebanon.

In a speech aired live Friday on Lebanese TV, Mikati said he hoped his departure would force other politicians to find solutions.

‘‘Today I announce the ­government’s resignation, ­hoping that God willing it will provide an impetus for the ­primary political blocs in ­Lebanon to assume their ­responsibilities,’’ he said.