Senedd CymruJoe Martin is Reform's MS for Caerdydd PenarthMembers of the Senedd from Plaid Cymru, Labour and the Greens walked out of a speech by a Reform MS on Wednesday where he joked that Welsh students are unable to read, and said Indian nurses were taking Welsh jobs.
It was the second day that Joe Martin had upset members in rival parties, after Plaid had accused him of "racism" over a speech on Tuesday claiming attacks from Sudanese asylum seekers were "inevitable".
Presiding Officer Huw Irranca-Davies rebuked the MS for Caerdydd Penarth for the second of the two speeches - but the BBC heard some in Plaid believe the Senedd's figurehead should have been firmer with Martin sooner.
Reform's Jason O'Connell said the walk-out was "shameful".
Earlier the party's chief whip defended Martin's speech in first minister's questions on Tuesday, telling political rivals to "get used to it".
In a Reform debate about international spending, Martin gave a speech where he mocked a list of examples of spending.
He said: "We send Uganda money to plant trees as well, because we won that competition, who can find the stupidest use of taxpayers' money"
He joked the same question was asked to "some Welsh students who had been through our underfunded education system, but we didn't get a reply because we emailed them and they couldn't read".
In response to interruptions from across the Senedd floor, he replied: "Have a look at illiteracy rates for students graduating."
Martin added it was great that nurses were being recruited from India "because it means that the Welsh people who would have otherwise become nurses can instead go on universal credit".
Plaid's Caerdydd Fynnon Taf MS Zaynub Akbar then said: "I'm going to leave this because I don't accept any of this and I don't want to be a part of it."
A Plaid source said most of the party's MSs who were able to leave did so. Mike Hedges from Labour and Welsh Green Party leader Anthony Slaughter also walked out.
Senedd CymruJoe Martin took part in a debate on international spending on WednesdayIn his response to the debate, the minister for the constitution, Dafydd Trystan Davies, said the debate had descended "to the level of a public house" at points.
Jason O'Connell from Reform said he was "deeply disappointed" at the walkout, which he called "shameful".
One source told the BBC that the overall tone of Martin's contribution, as well as the comment about Welsh students not being able to read, sparked the walkout among Plaid MSs.
Plaid Cymru's spokesperson said the party "will not stand by as Reform UK make a mockery of our democracy and mock the communities we represent".
Senedd CymruThe Senedd's debating chamber was left partially empty following Joe Martin's speechWednesday's walkout followed frustration, the BBC was told, among Plaid MSs over how Irranca-Davies had tackled the comments about asylum seekers from Martin on Tuesday.
Plaid had complained that the speech broke Senedd rules.
At the opening of the Senedd on Wednesday Irranca-Davies asked MSs to avoid language that has "the potential to inflame debate or to increase tensions", but did not initially reprimand him directly.
A Senedd spokesperson said no breach had been committed by the MS, although the BBC was told the presiding officer's comments could be construed as a final warning to all members.
After the second speech from Martin, the presiding officer Irranca-Davies did reprimand him, saying: "I would like you to reflect, please, on the remarks and your contribution today. It was not in line with my expectations."
The Greens' Anthony Slaughter said after the debate that Martin had been "completely disregarding the Llwywdd's opening statement today, showing a complete lack of respect for the Senedd and other members".
Reform had called for an end to all Welsh government spending overseas in the debate, which was rejected by Plaid and Labour.
On Tuesday, in a question to the first minister about the Welsh government's Nation of Sanctuary policy, Joe Martin made a series of allegations about Sudanese asylum seekers.
He raised a recent attack in Belfast, for which a Sudanese man appeared in court for earlier this month, and the murder of Rhiannon Whyte by a Sudanese asylum seeker.
He asked the first minister what he would do "to make sure that when the next inevitable attack happens, it doesn't take place in Wales".
Dan Thomas, Reform's Welsh leader, nodded as Martin made his contribution, but the remarks were greeted with gasps from Plaid Cymru and Labour members.
At the time the comments went without remark from the presiding officer, who is in charge of maintaining discipline in Senedd debates.
PA MediaLlŷr Powell is Reform's chief whip, in charge of party disciplineBefore Wednesday's events, Reform's chief whip Llŷr Powell said if there had been an incident like Plaid Cymru described on Tuesday then the presiding officer, also known as the Llywydd, "would have dealt with it there and then".
Powell said it was "bad form" to "put the spotlight on the Llywydd like this by leaking it to the press".
"I didn't hear anything I thought went over the line.
"I was talking about the Nation of Sanctuary during the election, Joe Martin was talking about the Nation of Sanctuary in the chamber."
He added: "Get used to it, it's the new norm are the words I use."
In a letter to the presiding officer, Plaid Cymru's minister for government business Heledd Fychan said the remarks were "dangerous and derogatory" which "brought the Senedd into disrepute".
Fychan, whose role is also known as the Trefnydd, added she would "always deal with instances of outright racism with the utmost seriousness and have written to the Llywydd seeking an urgent ruling on what I believe to be a serious and clear breach of Standing Orders".
Joe Martin has been approached for comment.
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