It was disrespectful for seven Labour MPs to announce their split from the party while colleagues are morning the death of Paul Flynn, an MP has said.
On Monday, seven MPs from constituencies in England announced they would form an "Independent Group".
Labour's Cardiff Central MP Jo Stevens said the party needed to "get rid" of its anti-Semites.
But she said problems should be tackled "collectively", and called for the group of seven to trigger by-elections.
The Newport West MP Paul Flynn died on Sunday.
At a press conference, one of the MPs who quit Labour, Luciana Berger, said the party had become institutionally anti-Semitic.
Ms Stevens said she would "absolutely not" be joining them.
The Labour Party is overwhelmingly the best way to secure a Britain which is just and fair. The impact of this morning’s development is to make that harder to achieve.— Jeremy Miles AC/AM (@Jeremy_Miles) February 18, 2019
"On a morning we in Wales and across the UK Labour Party are morning the death of our colleague Paul Flynn, MP for Newport West yesterday, I feel very sad, but I also feel to make this announcement this morning in the way my colleagues did is a bit disrespectful," she said.
"I think in order to change our party and make it better, and we do have some problems, we do have a problem in dealing with some anti-Semitism on our party, I believe we need to do that together collectively.
"We need to get rid of anti-Semites from the Labour Party."
She said party leader Jeremy Corbyn "needs to come out and say 'I absolutely will not tolerate anti-Semitism in the party', and to make sure that the party deals with the outstanding cases as quickly as possible".
"It might make anti-Semites in the party realise that they have no place in the party because they do not share our values."
A genuinely sad day. My friendships and campaigning on #Brexit and many issues go beyond parties and will continue to do so but I deeply regret the decision taken - not least at a time when our country faces greatest crisis since 1940, and we are mourning the loss of a colleague.— Stephen Doughty MP / AS (@SDoughtyMP) February 18, 2019
Wales' First Minister and Welsh Labour leader, Mark Drakeford, said the seven former Labour MPs should have stayed and fought for their views.
He said: "The real answer and the right answer is to stay and argue your corner and to make those arguments inside the party."
Mr Drakeford added: "My main reaction is one of sadness and disappointment."
Welsh Government cabinet minister Jeremy Miles said the Labour Party was "overwhelmingly the best way to secure a Britain which is just and fair".
"The impact of this morning's development is to make that harder to achieve," he added.
Stephen Doughty, Cardiff South and Penarth MP, said he deeply regretted the split, "not least at a time when our country faces its greatest crisis since 1940, and we are mourning the loss of a colleague".
But he said the party had "collectively failed" Luciana Berger, "who has endured the very worst anti-Semitic and bullying behaviour over the last years".
Pro-Corbyn Pontypridd AM Mick Antoniw accused the group of "self indulgent posturing".
But Blaenau Gwent AM Alun Davies said: "If there are any members of the Labour Party celebrating the loss of some talented, intelligent and committed MPs this morning or simply abusing them on social media then you don't understand what has happened to Labour."