Alun Cairns has apologised for his comments
The Conservatives have suspended Welsh assembly member Alun Cairns as a general election candidate.
A spokesman said an investigation was pending by the party chairman, and follows a row over a comment about Italians on a BBC radio programme.
Two Labour MPs have called on Mr Cairns to step down as a candidate for the Labour-held Vale of Glamorgan seat.
Mr Cairns quit his assembly education spokesman post and apologised for his "inappropriate" comments.
He likened Italians to "greasy wops" in a radio discussion on Euro 2008.
Mr Cairns, who is a South Wales West AM, also resigned as chair of the assembly's finance committee.
The Conservatives confirmed that Mr Cairns had been suspended as a candidate yesterday "pending an investigation by the party chairman".
Earlier, Caerphilly MP Wayne David said it was "a sensible and logical thing" for Mr Cairns to step down.
But Mr David, while welcoming the apology, said it was only partial if he remained a candidate in the Vale of Glamorgan.
"It's not the worst but nevertheless such terms are unacceptable," he told the BBC Wales Politics Show.
"If David Cameron wants to draw a line under it, it's very important for him to be absolutely clear that Alun Cairns isn't only stepping down from the two positions he holds but from the position he aspires to."
His comments were echoed by former Europe minister Denis MacShane MP, who added: "Xenophobic language against Italians is the same as other racism."
Mr Cairns apologised immediately for the comments made during BBC Radio Cymru's Dau o'r Bae discussion programme on Friday.
Contributors had been asked to say who they would be supporting during the Euro 2008 tournament.
When another contributor said she had written "nice food" next to Italy in the list, Mr Cairns said: "I've written greasy wops."
In a statement on Saturday afternoon, Mr Cairns, said: "I very much regret the remarks and wish to apologise once again for the offence they may have caused.
"I have the utmost respect for Italy and Italian people but accept that my comments, no matter how inadvertent, were unacceptable. "
Welsh Conservative leader Nick Bourne AM, who faces reshuffling his shadow cabinet in the assembly this week, said: "While his comments were completely out of character they were unacceptable."
Former Caerphilly MP Ron Davies, who is now the director of the Valleys Race Equality Council, said Mr Cairns had accepted his invitation to join their annual meeting next month, adding "I know there isn't a racist bone in his body.
"These comments he has made are inexcusable but we have to put them in the context of what was a light-hearted discussion around football and was meant, I'm sure, as laddish humour."