The president of Sinn Fein, Mr Gerry Adams, said last night that his party was looking forward to setting up the all-Ireland bodies and also looking forward to working with unionists.
Mr Adams said that Sinn Fein had policies for government and intended "to do our best for all the people of Ireland".
Ms Bairbre de Brun said that she viewed her position as Minister for Health, Social Services and Public Safety both as a great honour and as a challenge. "I want to take the opportunity to praise and pay tribute to all those who work in this area", she said, adding that speaking to these people in advance of yesterday had been an "inspiration".
She said that there was already considerable cross-Border co-operation in this area. "One of my priorities is to take the best from all areas in a co-ordinated approach."
Mr Martin McGuinness, who has been appointed Minister for Education, said that the people who had voted for Sinn Fein, "in concert with all sensible people on the island of Ireland", would be "overjoyed" at yesterday's events.
Mr McGuinness said he was proud and honoured to be "sent back to school" by his party leader and would do his best for all the children of Ireland, whom he viewed as "our most important natural resource". He added: "We have to nurture them, care for them and treat them with equality."
Despite having left school when he was 15, Mr McGuinness said that he had had a "political education of a lifetime", and he would incorporate this into his approach to education.
He said that he was in favour of integrated education and opposed to the 11-plus entrance examination. However, a review of this was pending, which he did not want to pre-empt.
Mr McGuinness accepted that some people would be "disquieted" that he had been entrusted with education, but he said that such things were not uncommon in conflict-resolution situations.
Mr McGuinness also said that he believed there were tens of thousands of DUP voters who were prepared to give him a chance.
However, later last night the Ulster Unionist chairman of the Assembly committee which will scrutinise Mr McGuinness said that there would be "deep anger, resentment and apprehension" over the appointment.
Mr Danny Kennedy said: "He will have an enormous amount to prove in terms of his peaceful commitment to education. My scrutineering role will be rigorous to ensure he acts properly and impartially."
Mr Kennedy claimed that Mr Peter Robinson, deputy leader of the DUP, could have secured the education portfolio, but had decided instead to become Minister for Regional Development.
The Sinn Fein chairman, Mr Mitchel McLaughlin, denied that the party had been "deliberately provocative" in appointing Mr McGuinness to the education portfolio.
There had been no late shift in ministerial choices, despite Mr McGuinness's appointment to the agriculture portfolio during the abortive attempt to set up the executive last July.
Mr McLaughlin added: "Sinn Fein has carefully planned its choice of ministerial posts with a systematic approach, because we want this Assembly to work. We have not set out to deliberately provoke, unlike some other parties. We have a genuine commitment to making the institutions and the Good Friday agreement work."