Both parties had earlier refused to back off after Mr Reynolds insisted Harry Whelehan, the Attorney-General, be appointed President of the Dublin High Court.
Labour backs wide-ranging changes in social legislation ranging from divorce to abortion and believes Mr Whelehan, a conservative Catholic, is not committed to them. In 1992, when in opposition, Labour sought Mr Whelehan's resignation over his pursuit of an injunction preventing a pregnant schoolgirl aged 14 from travelling to Britain for an abortion.
Recently Labour complained that Bills paving the way for a referendum on divorce were moving too slowly through his office.
Yesterday the two party leaders met but failed to resolve the dispute. A Cabinet meeting later delegated two ministers from each party to seek a compromise to avert the collapse of the coalition.
Labour has repeatedly warned that if Mr Reynolds invokes his Fianna Fail party's 9-6 Cabinet majority to appoint Mr Whelehan it will leave government. Labour ministers blocked a Cabinet meeting for several hours last month until the Whelehan appointment was taken off the agenda. Mr Reynolds denies he tried to 'bulldoze' the appointment, but insists Mr Whelehan is the only nominee and no solid argument against his appointment has been offered.
Both parties' unbending stance has made it difficult for either to back down without serious loss of face. For Labour the row is a measure of whether Fianna Fail will consult its partner as an equal. In July, Labour warned Mr Reynolds that he had damaged trust between the coalition parties after he publicly asserted that the judicial inquiry into alleged political favours in the meat industry had vindicated him before Labour was shown the 1,400-page report.
Labour later dubbed Mr Reynolds's 1987 handling of Iraqi export credits, a key issue in the inquiry, 'a policy disaster'.
Labour maintains that it helped Mr Reynolds off the hook earlier this year when it emerged that Irish passports had been awarded to members of a Middle Eastern family who invested IR pounds 1m in the Taoiseach's family pet food business, a transaction of which he maintained he was unaware.