Her remarks had apparently been prompted by a Friday column in the Hill that suggested Sen. Bernie Sanders and Elizabeth Warren against Trump in the 2020 election.
The Hill's social media account tweeted Budowsky's piece out on Saturday with the headline: "A Sanders-Warren ticket could win big in 2020".
Newsroom reported that Beresford confirmed she did send, and later delete, the tweets.
"They've learned nothing", she tweeted first, referring to the Democrats.
White House hosts meeting of Israeli, Arab officials on aid for Gaza
Trump's decision late past year to recognize Jerusalem as the capital of Israel, and to move the US embassy there from Tel Aviv. Jordan and Egypt, the only two Arab countries to have struck peace deals with the Jewish state, also participated.
Minutes later, she replied again: "No it couldn't".
On Saturday, Ms Beresford Tweeted that the Democrats - the opposition to the current Trump administration - needed to "get your s*** together or we will all die".
Beresford later deleted the tweets and locked her account, making it inaccessible to people who do not already follow her on Twitter.
In a brief statement, Foreign Affairs Minister Winston Peters said he was aware of the complaint and confident the Ministry was handling the response appropriately.
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FBI officials have recommended that the former number two at the FBI Andrew McCabe be fired, CBS News' Paula Reid reports. If McCabe is fired for a disciplinary reason, his full pension could be affected, or even forfeited entirely.
The Ministry of Foreign Affairs said it did not endorse the content or tone of the now deleted tweets and it expects its staff to remain politically neutral.
A representative for the New Zealand Embassy in Washington did not immediately respond to a request for comment Wednesday morning.
Beresford told Newsroom via email that she did write the tweets.
Caroline Beresford, New Zealand's deputy head of mission to the United States and ambassador to Haiti, sent the tweet in response to a post by U.S. politics website the Hill detailing the Democratic party's plans for the 2020 election and the possible pairing of Bernie Sanders and Elizabeth Warren as running mates.
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Those nominees for the MPC are Aisha Ahmad, Adeola Adenikinju, Aliyu Sanusi, Robert Asogwa and Asheikh Maidugu. It also noted that now , only three of them were valid, since the tenure of others expired last December.
Ms Beresford, second only to Ambassador Tim Groser in New Zealand's United States diplomatic contingent, has since made her Twitter account private.