into opening a public inquiry into President Trump's leading opponent, Joe Biden.
The messages come as Mr Trump faces a formal impeachment inquiry about it.
The exchanges show a senior diplomat saying it would be "crazy" to withhold military aid to Ukraine for Mr Trump's political gain in the 2020 election.
US law bans soliciting foreign help for electoral purposes.
But Mr Trump denies any wrongdoing and, on Thursday, publicly called on Ukraine and China to investigate Mr Biden and his son Hunter over their political and business dealings, even though he has not offered specific evidence.
He accuses his opponents of a "witch hunt".
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Impeachment in the House of Representatives would remove Mr Trump from office - but only if endorsed by the Republican-controlled Senate.
What do the texts say?
The impeachment inquiry stems from a 25 July call in which Mr Trump asked President Volodymyr Zelensky to investigate his rival.
The wide-ranging text message discussions are connected to allegations by the Democrats that Mr Trump dangled military aid as a way to press Ukraine to dig dirt on Mr Biden.
Sent between July and September, they involve high-ranking officials:
Kurt Volker, Mr Trump's Ukraine envoy who resigned a week ago
Gordon Sondland, the US ambassador to the European Union, and a significant donor to Mr Trump
Bill Taylor, a top US diplomat at the US embassy in Ukraine
On 19 July, the three diplomats discussed arranging a phone call between Mr Zelensky and Mr Trump.
Mr Volker told the other two he had had breakfast with Mr Trump's lawyer, Rudy Giuliani that morning - and identified the main purpose of the upcoming phone call.
"Most impt [important] is for Zelensky to say that he will help the investigation," he told the others.
But Bill Taylor, the senior US diplomat in Ukraine, warned that President Zelensky "is sensitive" about Ukraine being seen "as an instrument in Washington domestic, re-election politics".
Ahead of the call, Mr Volker texted that he had heard from the White House that it would result in a formal visit to Washington for Mr Zelensky, "assuming President Z convinces Trump he will investigate / 'get to the bottom of what happened in 2016'" - a reference to allegations of Ukrainian officials being involved in the US presidential election in 2016 which US intelligence agencies have blamed on Russia. Both Mr Trump and Russia have denied any involvement.
What were the diplomat's concerns?
We know from the call transcript that Mr Trump asked Mr Zelensky to investigate Joe Biden "as a favour".
But text messages show US officials discussed what the Ukrainian president should say in a statement afterwards.
By 13 August, Kurt Volker advised that Mr Zelensky's statement should address interference in US politics, "especially with the alleged involvement of some Ukrainian politicians" - and Burisma, the company Joe Biden's son was involved in.
There has been no evidence of wrongdoing by Hunter Biden.
Then, on 29 August, the tone of discussions changes. Mr Zelenksy's aide Andriy Yermak sent a curt message to Mr Volker, including a link to a Politico story headlined Trump holds up Ukraine military aid meant to confront Russia.
Mr Taylor, the senior diplomat in Ukraine, seemed to voice his concerns about the motives for the delay in a text on 1 September and a week later.
"I think it's crazy to withhold security assistance for help with a political campaign," he said.
That suggestion, however, was firmly pushed back by Ambassador Gordon Sondland, who said Mr Taylor was misunderstanding the president's intentions:
What are Democrats and Republicans saying?
In a letter alongside the release of the texts, top-ranking Democrats criticised Mr Trump's "now open defiance of our core values as American citizens."
"The President and his aides are engaging in a campaign of misinformation and misdirection in an attempt to normalise the act of soliciting foreign powers to interfere in our elections," it said.
"This is not normal or acceptable. It is unethical, unpatriotic, and wrong."
But Republican Jim Jordan said the Mr Volker's testimony on Thursday had "undercut the salacious narrative that Representative Adam Schiff is using to sell his impeachment ambitions".
Mr Jordan heads the House Oversight Committee which tweeted that "this information [contained in the text messages] cannot possibly be understood without Volker's explanations from yesterday's testimony".
He has called for the entire transcript of the testimony to be released.