A whistleblower complaint said that Trump sought to use military assistance for Ukraine to push President Volodymyr Zelensky to investigate Biden, who is now running to be the Democratic Party's 2020 presidential candidate.
The chairmen's 13 document requests also included any information about a White House meeting on May 24 that involved Kurt Volker, the special envoy to Ukraine at the time; Pence's September 18 call with Zelensky; and any information about the actual or potential withholding, freezing, or other actions of foreign assistance of any kind to Ukraine for fiscal year 2019.
According to a White House memorandum of a July 25 phone call, Trump asked Ukrainian President Volodymyr Zelensky for what he called "a favor" - an investigation into Biden and into Ukraine's supposed role in helping Democrats in the 2016 election.
"Recently, public reports have raised questions about any role you may have played in conveying or reinforcing the president's stark message to the Ukrainian president", Messrs Cummings, Schiff and Engel wrote in a letter to Mr Pence.
"I don't care about politics", he said.
If Democrats manage to impeach Mr Trump - by way of a vote in the House of Representatives - a trial would be held in the Senate.
But in a move to crank up the pressure on the president, the three House committees leading the investigation have given him until 18 October to hand over the documents.
Trump received support from Secretary of State Mike Pompeo, who dismissed questions about Trump's attempts to push Ukraine and China to investigate Democratic rival Joe Biden as a "silly gotcha game".
A spokeswoman for Mr Pence said the broad nature of the request showed that it was not "serious".
Democratic Representative Raja Krishnamoorthi, a member of the Intelligence Committee, said he believed the whistleblower's identity should be kept secret even from members of the panel.
The investigation could lead to the approval of articles of impeachment - or formal charges - against Trump in the House.
When Mr Pence met with Mr Zelenskiy, the two discussed the $US 250 million in security assistance that the US Congress had approved but that the Trump administration had not disbursed.
The White House has planned to send a letter to House Speaker Nancy Pelosi, D-Calif., arguing that Congress can not undertake an impeachment investigation without first having a vote to authorize it.
But that outcome is seen as unlikely given that the president's fellow Republicans control the Senate.
President Donald Trump apparently has no intention of backing down when it comes to protesting the ongoing impeachment inquiry.
A cache of diplomatic texts Democrats received as part of their impeachment inquiry showed United States officials pressured the Ukrainian government to launch investigations that might benefit Trump's personal political agenda in exchange for a meeting of the two countries' leaders.
The release followed a 10-hour interview with one of the diplomats, Kurt Volker, who stepped down as special envoy to Ukraine after the impeachment inquiry had begun.
Trump pushed back hard, saying there was no quid pro quo and, in an effort to recast the entire saga, insisted it was his responsibility to investigate "corruption".
Most Republican senators remained quiet on Friday, but the 2012 presidential candidate and current Utah senator Mitt Romney issued a statement that said "the president's brazen and unprecedented appeal to China and to Ukraine to investigate Joe Biden is wrong and appalling". Trump has called the impeachment investigation a "hoax" and accused the media and Democrats of corruption.
"Speaker Pelosi has confirmed that an impeachment inquiry is underway, and it is not for the White House to say otherwise", the letter said.
Mr Biden leads in most opinion polls among the 19 Democrats seeking the party's nomination. "I am not going to stand for it", Biden said at a campaign event in Los Angeles, deeming Trump "unhinged".
In a signal of how Kiev will handle investigations being watched in Washington, Ukrainian prosecutors said they would review 15 old probes related to Burisma's founder but added that they were unaware of any evidence of wrongdoing by Mr Biden's son.