If they do not comply with the next few weeks, subpoenas will be issued.
With his announcement, Mr Nadler is taking a shotgun approach to his investigations of the president, the BBC North America reporter Anthony Zurcher says.
He says the press release announcing the investigations doesn't mention Russia or its election-meddling by name.
But the key components of the collusion allegations - the 2016 Trump Tower meeting, the WikiLeaks email dumps, changes to Ukraine policy in the Republican Party platform and the Trump-Russia business dealings - are all over the document requests.
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