Ireland has voted to remove the crime of blasphemy from its constitution by a significant majority, according to exit polls.

The national broadcaster, RTÉ, suggested that just over 71% had voted yes on the question of whether or not to repeal the constitutional ban. The Irish Times poll predicted that 69% had backed the proposal.

Official counting of the votes beings on Saturday.

The blasphemy referendum was held alongside a presidential election, in which exit polls suggested the incumbent, Michael D Higgins, had won by a landslide.

Should the referendum figures be confirmed, the move would be the latest sign of the weakening of religious conservatism in the country.

The last prosecution for blasphemy in Ireland was in 1855, but three years ago Irish police investigated comments made by Stephen Fry on television in which the comedian described God as “capricious”, “mean-minded”, and an “utter maniac”. The investigation was later dropped after police decided insufficient numbers of people had been outraged.

Ireland voted to allow same-sex marriage in 2015, and nearly two-thirds of Irish voters backed the repeal of the country’s abortion ban in May this year, leading the taoiseach, Leo Varadkar, to proclaim the “culmination of a quiet revolution for the past 10 or 20 years”.

An RTÉ exit poll on the presidential election suggested Higgins had secured more than 56% of the vote.

The results put the controversial businessman and former Irish Dragons’ Den investor, Peter Casey, in second with about 20% of the first-preference vote. It means Higgins is likely to be easily re-elected for a second seven-year term on the first count.

The results also indicate that the Sinn Fein MEP Liadh Ni Riada received 7.4% of the vote, senator Joan Freeman 6.3%, the businessman and former Dragons’ Den panellist Sean Gallagher 5.5% and businessman Gavin Duffy 2%.

The Irish Times poll, conducted by Ipsos/MRBI, questioned more than 4,300 voters outside 160 polling stations across the country. It produced broadly similar projections.

The results of both polls were published at 10pm as polling stations closedMore than 3.2 million people were entitled to vote in 40 constituencies across the country.

Opinion polls throughout the campaign consistently placed Higgins as the favourite, despite being plagued by questions over presidential expenses.If re-elected, the 77-year old will become the fifth Irish president to serve for two terms.