The Ulster Unionist Party has advised its voters to give their lower vote preferences to "any candidate they trust".
It came after the DUP demanded to know whether UUP leader Mike Nesbitt was backing transfers going to other unionist parties.
DUP leader Arlene Foster said she had "no hesitation" in asking her own party's voters to transfer to other unionist parties.
She added: "I'm not sure where the UUP stands on this."
The former First Minister suggested the UUP chief might prefer votes to go to fellow opposition parties such as the SDLP or Alliance.
She said the UUP was not running enough candidates to emerge as the largest unionist party.
Referring to any developing relationship between Mr Nesbitt and SDLP leader Colum Eastwood, she asked: "If the choice is 'get Arlene' or 'get Colum', which would Mike prefer?"
And in light of Mr Eastwood's call for joint authority between London and Dublin rather than any return to direct rule, Mrs Foster urged Mr Nesbitt to answer: "Does he stand by those who believe in the Union or those who push for joint authority?"
A UUP statement insisted, however: "We are making no assumptions about who an angry electorate will support on March 2, but we are running sufficient candidates to emerge as the leading party of unionism.
"As for transfers, we have been clear. Ulster Unionist voters should give their lower preferences to any candidate they trust to do what's right by their constituency and Northern Ireland."
On Monday, as he launched the SDLP's election campaign, Mr Eastwood urged voters to reject the DUP/Sinn Fein coalition that has governed for the last decade and instead give his party and the Ulster Unionists another chance to lead.
Mr Nesbitt also responded to demands from Sinn Fein over its stance on an Irish Language Act, which Mrs Foster has stressed she will never allow.
Former Culture and Arts Minister Caral Ni Chuilin said: "We now need clarity from Mike Nesbitt and the UUP on their position on an Irish Language Act.
"Do they accept it as part of the St Andrew's Agreement or are they going to follow behind the DUP in attempting to deny people's rights?"
Mr Nesbitt said: "We bear no ill-will to those who cherish the Irish language.
"Indeed we supported commitment to the language in the 1998 (Good Friday) Agreement which we have honoured in full.
"The Act was a product of the DUP's negotiations at St Andrews.
"In the current financial climate, we could not justify the costs associated with an Irish Language Act but again stress that we have no difficulty with those who wish to speak the language."