Four days later, Mr. Sondland texted Mr. Volker, asking if they still wanted the Ukrainian president “to give us an unequivocal draft” specifically citing the two issues that Mr. Trump has been focused on: Burisma, the Ukrainian energy company that had put Mr. Biden’s younger son, Hunter Biden, on its board, and Mr. Trump’s belief that Ukraine had interfered in the 2016 American elections to benefit Hillary Clinton.

Mr. Volker replied: “That’s the clear message so far …”

Under questioning on Capitol Hill, Mr. Volker told House Democratic investigators that the language including specific references to Burisma and the 2016 election had come from Mr. Giuliani, the person familiar with his testimony said.

Mr. Volker told the House investigators that the Ukrainians had earlier proposed language promising a statement on fighting corruption that did not specifically mention Burisma and 2016. When Mr. Giuliani was shown that original language, Mr. Volker told the House, he indicated to Mr. Volker that it was not sufficient and said the Ukrainians should be asked for specific public commitments to investigate Burisma and 2016.

By Mr. Volker’s account, according to the person familiar with his testimony, he was eventually told by Mr. Yermak that the Ukrainian government could not agree to the language being sought by Mr. Giuliani. Mr. Volker told Mr. Yermak that he was right, and the idea was dropped, according to the account Mr. Volker provided the House.

The idea behind the statement was to break the Ukrainians of their habit of promising American diplomats and leaders behind closed doors that they would look into matters and never follow through, the people briefed on it said. According to the account provided by Mr. Volker to the House, the idea of the Ukrainians providing a statement had originated with Mr. Giuliani in a conversation he had with Mr. Yermak.

It is unclear if the statement was delivered to Mr. Zelensky, but no statement was released publicly under his name. Around that time, the Ukrainian officials indicated to the Americans that they wanted to avoid becoming more deeply enmeshed in American politics.

The drafting of the statement, which came in the weeks after the July 25 phone call between Mr. Trump and Mr. Zelensky, was an effort to pacify Mr. Trump and Mr. Giuliani and to normalize relations between the two countries as Ukraine faced continuing conflict with Russia. Mr. Sondland and Mr. Volker believed that Mr. Giuliani was “poisoning” Mr. Trump’s mind about Ukraine and that eliciting a public commitment from Mr. Zelensky to pursue the investigations would induce Mr. Trump to more fully support the new Ukrainian government, according to the people familiar with it.