His firm request follows months of parliamentary stalemate, and suggests that general elections could take place before the deadline of February next year.
Mattarella spoke after meeting Senate Speaker Pietro Grasso and President of the Chamber of Deputies Laura Boldrini, and asked them both to convey the urgency of the votes to Italy's House and Senate.
"The head of state underlined the necessity for parliament to proceed urgently with two important institutional duties," said the Quirinale presidential palace in a statement. As well as approving the electoral law, both chambers also need to appoint a Constitutional Court judge.
"The President of the Republic asked the Presidents of the Senate and the Chamber of Deputies to convey the urgency to their respective parliamentary groups," the statement continued.
Italy's Constitutional Court ruled in January that the new electoral law was legitimate, saying it would be "immediately applicable" - and removing the biggest obstacle to holding elections.
When ex-Prime Minister Matteo Renzi stepped down in December following a failed referendum, opposition parties called for general elections immediately, but Mattarella has held off on calling them until after the ruling on the new electoral law (Italicum).
This is because the law had been drawn up to apply only to apply to the Lower House, because the Italian Senate was set to be reformed under a set of constitutional reforms proposed last year. Hearings on Italicum's constitutionality had been postponed to avoid interference with the referendum.
When these proposals were overwhelmingly rejected in December's referendum, the perfect bicameral system was preserved - leaving the country without a workable electoral law.
In January's ruling, the Constitutional Court declared as illegitimate those aspects of Italicum which did not fit the bicameral system, but ruled that an amended version of the law was applicable.
However, Mattarella is unlikely to call for elections until both houses of parliament have approved the law.
Paolo Gentiloni's caretaker government is currently in power in Italy, with elections set to be held by February 2018 at the latest, but likely to be called sooner.