The Democratic Unionist Party (DUP) is the only party strong enough to unite unionism, according to Arlene Foster.
The DUP leader was speaking at the launch of her party's local government election manifesto in Belfast.
She argued that every first preference vote for another unionist party "runs the risk of dividing unionism".
She said it also risked "returning fewer unionist councillors" and "bolstering Sinn Féin demands for a divisive" Irish border poll.
'No free hits'
The DUP deputy leader Nigel Dodds rejected the argument that unionists who disagree with his party on social and moral issues or Brexit can feel free to register a protest at the council elections on 2 May.
He said that was because the job of Stormont first minister is not at stake.
There is "no such thing as a free hit" when it comes to elections, he added.
On councils, the DUP commits in its manifesto to what it calls a real-terms cut in rates by keeping any rises below the level of inflation over the full council term.
'More inclusive playparks'
The manifesto states that there should be further discussion on whether councils should get additional powers to regenerate towns and villages.
But it says that if this happened there will have to be improved protections for minorities.
It argues that those already in place have proved highly ineffective in protecting unionists in western and border areas.
The DUP also wants to see more playparks and leisure facilities made fully accessible for people with disabilities.
The party says it is not good enough that while there are nearly 900 playparks, in some council areas only 105 of those facilities have inclusive play equipment.
On Brexit, the DUP manifesto states that the UK's vote to leave the EU must be honoured but Northern Ireland cannot be subjected to onerous new trade barriers within the UK.