In Dublin, the Iseq index ended at 6,640.10 points, up 0.5% on the day, helped by gains for Bank of Ireland.
The index has now climbed 20% from its 12-month low on June 24, the day after the UK voted to quit the EU.
After touching an all-time record high of 7,338.49 points, the Ftse ended the session at a record closing level of 7,337.81 points, up 0.6% on the day.
“There are people who want to say this is the moment it’s going to turn around, but each day they get proven wrong,” said IG market analyst Josh Mahony.
He said a likely further devaluation of the pound in the next few months would support the index higher. “But the gains are not exuberant.”
Brokers pushed broadcaster ITV towards the top of the Ftse winners. Goldman Sachs added the broadcaster’s stock to its “conviction list”, saying it is a likely target for mergers and acquisition activity.
The broadcaster was also one of JP Morgan’s top picks in the European media sector.
House-builders also helped the Ftse rally, with house improvement retailer Kingfisher marking its best daily gain since September. Barratt Development led sectoral gains, while Persimmon and Taylor Wimpey also gained 1.4% and almost 1%, respectively.
“If you want to sleep at night, you’d probably buy a Persimmon or Taylor Wimpey. If you want a bit more rock and roll, you might buy a Redrow or a Bovis [Homes],” said Jefferies analyst Anthony Coding.
Pharmaceuticals were buoying the index, rebounding after being weighed down earlier this week by US president-elect Donald Trump’s criticism of high drug prices in the US, and after a meeting of executives of companies to discuss caps on price increases.
Shares in pharmaceutical maker Shire were up 2.3%, and peers AstraZeneca and Hikma also gained, up 2% and 1.2%.
Rolls Royce dragged on the index, down more than 2%, while precious metals miners Randgold Resources and Polymetal International fell around 1.4%, tracking the price of gold, which was down from a 7-week high.
Building materials supplier SIG surged to the top of the mid-cap index, up over 16% after it reported higher full-year sales.
Its shares marked their biggest one-day gain since March 2009. Blue chip Travis Perkins was up 3% and peer Grafton surged by 8.4%.
Reuters and Irish Examiner staff.