Mike Hedges reiterated his support to the Labour leader, calling for opponents to stand against him if they think they can do a better job.
A statement by Mr Hedges was read out at a rally of supporters of Mr Corbyn outside Welsh Labour's headquarters in Cardiff on Friday.
It comes after a week of turmoil in the party, with mass resignations from the shadow cabinet.
Despite repeated calls for his resignation, and losing a motion of no-confidence among his MPs, Mr Corbyn has stayed in place.
Pontypridd MP Owen Smith and Angela Eagle, MP for Wallasey, are considering leadership bids if he does not resign.
Mr Hedges, AM for Swansea East, said ordinary members overwhelmingly wanted Mr Corbyn as leader: "Thousands joined the Labour party in order to support him".
He said, in a statement read out at the rally at Transport House: "Has Jeremy made mistakes? Of course he has, all new leaders do.
"Remember when we had a Labour leader who could not eat a bacon sandwich?
"If someone thinks they can do a better job than Jeremy is doing, their option is straight forward. Go and get the required number of nominations from MPs, stand and let the members decide.
"Put crudely, put up or shut up."
The rally was told the statement had the support of Jenny Rathbone, Cardiff Central AM, but neither attended.
Speakers included Darren Williams, a Cardiff Labour councillor who sits on Labour's national executive committee.
He said the party needed to return to "full mandatory reselection", calling for MPs to "pay with their jobs for what they've done".
"We must never forgive or forget what's been done in the last few days," he said, adding Mr Corbyn has been put under "intense pressure by careerists and backstabbers".
PCS Wales Secretary Shavanah Taj said the 60,000 people reported to have joined the party in the last week "haven't joined the Labour Party because of Angela or Tom".
Among those who attended was Hedley McCarthy, former Blaenau Gwent Labour leader and a county councillor, who said Mr Corbyn had been "treated abysmally".
"They are showing no respect for the membership of the Labour Party," he added.
One organiser of the rally of said he believed about 300 people attended.
Earlier this week, First Minister Carwyn Jones said it would be very difficult for him to carry on as leader if he faced the same situation as Mr Corbyn.
Opponents of Jeremy Corbyn need to "put up or shut up", a Labour AM has said.