Bobby Deacy, the IRFU president who accepted Kidd's resignation, said: "I wish to thank him for his contribution and efforts with the team and I wish him well for the future."
The meeting involved Kidd, Deacy and his fellow IRFU members Eddie Coleman, John Lyons and Philip Browne, the secretary-treasurer.
The All Black Mike Brewer, who coaches Blackrock College, and Dave Haslett, the Irish A team coach, are possible replacements.
Kidd's position came under threat after Ireland's 37-29 defeat by Italy at Lansdowne Road on Saturday. That was Ireland's sixth defeat in their last seven matches under the New Zealander, who was appointed Ireland's first full-time paid coach 15 months ago.
Ireland, who finished bottom of last season's Five Nations' Championship, kick off this year's campaign with a daunting game against France in Dublin on 18 January.
Scott Gibbs will captain Wales for the first time when he leads the national side against the United States at Cardiff Arms Park on Saturday. The Swansea centre takes over from the Cardiff hooker Jonathan Humphreys, who has decided not to appeal against a seven-day ban following his sending-off in Sunday's European Cup semi-final defeat at Brive.
Garin Jenkins has been elevated from the replacements bench to play instead of Humphreys. The Swansea hooker wins his 31st cap. Barry Williams, of Neath, is the new replacement hooker.
Wales' coach, Kevin Bowring, said: "I have used this as an opportunity for someone to gain personal development from the situation, rather than go to a tried and trusted captain."
Gibbs has played just three Tests after returning from rugby league with St Helens.
Bowring felt that Humphreys had been "very sensible" to drop his appeal against his suspension. The 27-year-old hooker said: "As captain of Wales, I am mindful of the need to set an example and will accept the adjudicator's decision, even though it is very painful to take."
The flanker Ian Smith will miss the opening match of Scotland's Five Nations' Championship after breaking his thumb while playing for Gloucester. Smith had hoped to recover from the injury suffered in a Pilkington Cup game against Leeds last month in time for Scotland's opener against Wales at Murrayfield. But Smith, who has won 20 Scottish caps, had to undergo surgery to pin the broken bone and it will not be removed until the day of the match in two weeks' time. It will be the first full Scottish international Smith has missed since the 1995 World Cup finals.
Andy Robinson will combine his Bath playing and coaching roles at least for the remainder of this season. The former England flanker lines up against Anglo-Welsh Cup opponents Swansea tonight as one of six Bath internationals on show.
"It is important I maintain my fitness," said Robinson, who on Monday succeeded Brian Ashton as Bath's full-time head coach. "I am needed as cover for our other open-side flanker, Nathan Thomas."Reuse content