McIlroy, who completed a career Grand Slam of major titles at Augusta National in April, carded four birdies to stay in touch with France's Adrien Saddier, who also posted a round of 68 at the par 72, 7441-yard K Club course near Dublin.
Italian Open champion Saddier led by a shot from Angel Hidalgo, who carded 12 birdies in a superb nine-under round of 63 that catapulted the Spaniard into title contention.
Another Spaniard, Alfredo Garcia-Heredia fired a 67 to sit three shots off the pace, but overnight leader Joakim Lagergren slipped to four back with a round 73.
McIlroy, bidding to win his second Irish Open title, was unhappy despite a second consecutive round without a bogey.
"As I was walking off the 18th green, I said to Harry (Diamond, his caddie), this is probably the most frustrating four-under par round of golf I've played in a while," said the Northern Irishman.
The 36-year-old McIlroy, the world number two added: "I feel like all day I was just trying to keep myself in a close position to the lead. I feel like I could be a couple of shots better, but overall I'm still in a decent position going into tomorrow."
An elated Hidalgo, who equalled a European Tour record by becoming the 12th player to card 12 birdies in a single round, said: "I really feel for a few moments I was playing the PlayStation, to be honest. Every single shot was directly to the pin."
The 33-year-old Saddier, playing in the final group after starting the day one shot behind Lagergren, mixed seven birdies with three bogeys.
"I was quite surprised with the score to be honest," said Saddier. "But I think, yeah, I managed the course pretty well, with my low moments and my high moments. So I feel happy about that 68."
Saddier, who led after two rounds of last week's European Masters in Switzerland before fading, added: "There is still 18 holes to play, so a lot of things can happen. As I said yesterday, I crushed myself last weekend."