Plaid Cymru leader Leanne Wood says the party takes bullying "very seriously" but will follow due process after an AM was suspended as a councillor.
A tribunal ruled Neil McEvoy's behaviour to be bullying after an officer said she felt threatened by a comment he made after an eviction case.
Plaid officials will meet the South Wales Central AM to discuss the issue.
In a speech to the Plaid conference, Mr McEvoy urged the party not to throw its own members "under the bus".
Fellow AM Bethan Jenkins had questioned whether he should have been allowed to address the event in Newport, while two other AMs have told BBC Wales Mr McEvoy should be suspended from the party pending inquiries.
Plaid Cymru will decide whether to take any action against Mr McEvoy next week.
"We take bullying very, very seriously in Plaid Cymru, but we also take process very seriously," Ms Wood told BBC Wales.
"This is a matter now that has been referred to the party chair, there is a process being undertaken and I respect that process.
"And it's important that all of us respect that process now."
At a tribunal on Friday, the Adjudication Panel for Wales ruled Mr McEvoy broke Cardiff council's code of conduct but did not bring the council into disrepute following an incident outside the city's civil justice centre in July 2015.
A council officer said she had felt "threatened" by a comment Mr McEvoy made after he supported a council tenant at an eviction hearing.
Ms Jenkins questioned whether the scheduled speech by the South Wales Central AM to Plaid Cymru's spring conference in Newport on Saturday should go ahead in light of the judgement.
Mr McEvoy spoke at a lunchtime fringe meeting on equality and went ahead with a speech to the full conference on Saturday afternoon, saying: "I'm still here."
He said Plaid Cymru should "do what it takes to beat the Labour Party in Wales", questioning his party's decision to support Carwyn Jones's administration with the "compact" agreement.
In an apparent reference to calls for his suspension from the party, Mr McEvoy said Plaid had to decide if it was the sort of party that "throws its own members under the bus".
After the hearing on Friday, Mr McEvoy described the panel proceedings as a "farce" but Plaid chairman Alun Ffred Jones said the matter was "serious because it involves bullying".
Mr McEvoy told BBC Wales he would not respond to anonymous calls for his suspension from the party but insisted everybody should respect his freedom of speech.
"I would invite those people to come and speak to the resident who was evicted," he said.
Asked how he would react if Plaid suspended him, he said: "I don't want to get into that."
Labour AM Rhianon Passmore called on Ms Wood to suspend Mr McEvoy, writing to express her "shock and serious concern" that he was allowed to speak at the event.
"By allowing Neil McEvoy not only to attend Plaid's conference but to address it, your party appears to condone his behaviour," she wrote.