CAIRO, Jan 18 (Reuters) - More than 98 percent of voters backed a new Egyptian constitution in a referendum this week, authorities said on Saturday, though the turnout was lower than some officials had indicated, with under 40 percent of the electorate taking part.

The vote advances a transition plan that the military-backed government unveiled after deposing Islamist president Mohamed Mursi last July following mass unrest over his rule.

"Now that God has supported us in legalising our constitution, we ask for his aid in achieving the remaining two stages of the road map: the presidential and parliamentary elections," said Nabil Salib, head of the Supreme Election Committee.

The "yes" vote was 98.1 percent, and 38.6 percent of eligible voters took part, Salib told reporters.

The turnout was well below the 55 percent that an Interior Ministry official had estimated after the two days of voting closed on Thursday. However, it exceeded the 32.9 percent turnout in a referendum that backed the previous Islamist-tinged constitution under the Muslim Brotherhood's Mursi in 2012.

The new constitution, which won wide support from many Egyptians who favoured Mursi's removal, could lead to an outright ban on Islamist parties and strengthens the political grip of the already powerful military establishment.

The Muslim Brotherhood, which has been designated a terrorist organisation and faces a wide crackdown from security forces, boycotted the vote and accuses the army of having staged a military coup against Mursi last year.

The new constitution allows a presidential election to be held before parliamentary polls, a change in the transition plan announced by the army in July.

Interim President Adly Mansour is expected to announce within days which election will come first.

Army chief General Abdel Fattah al-Sisi led the July 3 overthrow of Mursi and is widely seen as the front-runner for the presidency. He is expected to announce his candidacy within a few days. (Reporting by Ahmad Tolba and Asma Alsharif; Editing by Kevin Liffey)