The Welsh first minister, Carwyn Jones, may be recalled to the inquest into the death of Carl Sargeant to give more details about the pastoral care that was offered to the senior politician.

Jones told the inquest that another Labour politician, Ann Jones, had been asked to stay in touch with Sargeant in the days after he was sacked over allegations of inappropriate sexual behaviour.

Leslie Thomas QC, representing Sargeant’s family, told the court the first minister had appeared to testify that he spoke to Jones over the weekend after the sacking, but Thomas said that Ann Jones had now provided a statement to the inquest claiming there were no phone conversations between them. Thomas asked for the first minister’s telephone records to be made available when the inquest resumes in the new year.

Sargeant, 49, was found dead at home four days after he was dismissed as the Welsh cabinet secretary for communities and children in November last year.

On Friday, Lesley Griffiths, the Welsh cabinet secretary for energy, planning and rural affairs, told the inquest she did not believe enough pastoral care had been given to Sargeant after he was sacked. She said she thought there should be a formal support network in place for sacked ministers.

Griffiths, a close friend of Sargeant, said he was caring, optimistic and sensitive. She told the court she knew there had been a “significant life event” in his family. “I saw him break down and cry on more than one occasion,” she said.

Griffiths said Sargeant had taken up crocheting to relax on long train journeys between their constituencies in north Wales and the assembly in Cardiff. And in the summer before Sargeant died, he told her during a meal in Cardiff that the “black dog” had visited and that he had consulted a doctor about depression.

Griffiths said Sargeant had felt he was being watched carefully, as if his job was under threat. “You could see it was getting him down. I think he felt undermined,” she said. After he was sacked, Griffiths said, Sargeant was in an awful way, but she never thought he would take his own life.

The coroner, John Gittins, suggested to Griffiths that there did not appear to be a formal support network in place for sacked ministers. She replied: “That’s true,” and said she believed there should be one.

The coroner said people had a moral and social responsibility to support those who had been sacked from prominent positions, and he asked the minister if she agreed. Griffiths replied: “Yes.” Asked by Thomas whether she thought there ought to have been more pastoral care for Sargeant after his sacking, she answered: “Yes, I do.”

Cathryn McGahey QC, counsel for the first minister, asked whether Griffiths had ever heard reports of Sargeant drinking too much and “getting silly” with women. She replied: “No.”

The inquest had been due to end on Friday, but the court was told there would be a challenge from the first minister’s legal team over the coroner’s decision not to allow evidence to be heard relating to text messages allegedly sent by a north Wales councillor about Sargeant.

Bernie Attridge, the deputy leader of Flintshire county council, allegedly sent a text in which he appeared to suggest Sargeant would be “shitting bricks” because politicians were coming under scrutiny as part of the #MeToo movement.

The coroner said he would recall the first minister’s senior special adviser, Matt Greenhough, in the new year. Jones may also be recalled.

A spokesperson for the first minister said: “It is right and proper that the inquest is conducted fairly and openly and the coroner considers all relevant evidence available to him.”

In a statement issued after the hearing was adjourned, Neil Hudgell, a solicitor advising Sargeant’s family, said: “We are shocked and concerned by new witness evidence which appears to contradict evidence already given on oath by the first minister and his senior special adviser.” They said they should return to court to clarify the contradictions.

The statement continued: “For Bernie, Jack, Lucy [Sargeant’s wife, son and daughter] and family, it has been a long and difficult week full of unnecessary delays, and it is highly unsatisfactory that they have not yet been able to get all the answers they deserve. However, they are undeterred and will not stop in their quest for the truth.

“I feel the need to remind everyone as it seems to have been forgotten at times this week that at the heart of these proceedings is a much loved and missed husband, father, son and brother.”

The inquest is due to resume in January.

• In the UK, the Samaritans can be contacted on 116 123. In the US, the National Suicide Prevention Lifeline is 1-800-273-8255. In Australia, the crisis support service Lifeline is 13 11 14. Other international suicide helplines can be found at www.befrienders.org