High-ranking National MP Paula Bennett says if the Greens don't have anything nice to say about Donald Trump, they should keep their mouths shut.
But co-leader Metiria Turei says she'd rather not congratulate a "sexual predator", no matter what he's achieved.
The Greens on Thursday refused to support a Government motion congratulating the Republican nominee on his shock victory in the US election.
"We vow to fight the climate change denial, the misogyny, the racism represented by Trump," Ms Turei told Parliament.
The motion was passed 106-14, with the Greens the only party voting against it.
Speaking to Paul Henry this morning, Ms Bennett said democracy had spoken.
"The people of America have elected a President, and Trump is it and that should be treated, quite frankly, with the respect that it deserves in that position."
With Labour and the Greens working together to topple National at next year's election, Ms Bennett said Ms Turei has to be "a grown-up" if she wants to be a part of Cabinet.
"If you haven't got something nice to say, don't say anything at all. In this case I actually think it was offensive to the people of America, who have in a true democracy chosen a leader."
Labour deputy leader Annette King, appearing on the show alongside Ms Bennett, believes defeated rival Hillary Clinton struck the right tone in her concession speech.
"She said he is the elected President, he must be given a chance to be a President and people need to get behind him," she said.
"I think it was unwise politics, because we've got to look to the future. We will deal with all sorts of countries, whether it's China or Russia or wherever… as a small nation, and we've got to look beyond the person to what we hope is going to be a continuation of good democratic practises in the United States."
Ms Turei told Newshub the Greens did not believe they could "in good conscience and in response to our supporters, vote for the motion".
"The majority of Americans who voted actually voted for Hilary Clinton, which makes me appreciate even more our proportional MMP system that allows a diversity of views to be represented in Parliament.
"Paula Bennett is entitled to congratulate a sexual predator if she chooses and she should respect my right not to."
Neither Ms Bennett nor Ms King mentioned Ms Clinton's victory in the popular vote.
Ms King refused to rule out giving the Greens spots in Cabinet should the two parties form the next Government.
Ms Bennett did not speak during the brief debate on Thursday's motion, leaving it to Steven Joyce to do all the talking.
Ms King spoke for Labour, calling on Mr Trump to "uphold the rule of law, the principle of equal rights and dignity, freedom of expression, respect, inclusion, and understanding, because these are the values that lie at the heart of a liberal democracy".
The Maori Party tempered their support for the motion, co-leader Marama Fox calling it "a little bit difficult".
"The brick layers are going to be happy and the concrete merchants will be happy, because they will be building a wall very soon to keep Americans in," she told Parliament.
"And that might be because, if you watched the results as they came in overnight, you would have seen that a number of immigration sites around the world actually crashed from the inquiries of people trying to get out."