The impeachment inquiry into Trump began when a whistleblower reported that Trump had pushed Zelensky to launch a public investigation into the Biden family's dealings in Ukraine - specifically, why the former vice president pressured former Ukrainian President Petro Poroshenko to fire a top prosecutor, Viktor Shokin, who was investigating Ukrainian natural gas firm Burisma Holdings.
"The investigation isn't going to end", Schiff said.
"That investigative work will go on but what we're not prepared to do is wait months and months while the administration plays a game of rope-a-dope in an effort to stall", he said.
Schiff argued on CNN's "State of the Union" that while his committee has no more public testimony scheduled, he doesn't "foreclose the possibility of others" being added in the impeachment inquiry of President Donald Trump.
This second panel will then draft articles of impeachment to go before the full, Democrat-controlled House, which is expected to impeach the president, leading to a trial in the Senate.
Trump's administration has refused to provide documents requested by House Democrats and blocked witnesses from testifying including Secretary of State Mike Pompeo, former national security adviser John Bolton and acting White House Chief of Staff Mick Mulvaney.
Schiff said "it's important to know we're not stopping" while saying again the evidence is overwhelming.
A number of Democrats on the House Intelligence Committee have commented that the president is welcome to testify before the committee during the impeachment hearings.
Democrats also are looking into whether Trump abused his power by withholding $391 million in security aid to Ukraine - a vulnerable USA ally facing Russian aggression - as leverage to pressure Kiev into conducting the two investigations that could be politically beneficial to Trump.
Trump is running for re-election in 2020.
"Even as we compile this report, even as we submit evidence to the Judiciary Committee, we're going to continue our investigation", he said on NBC's "Meet the Press". He contended that if President Barack Obama had acted like Trump on Ukraine, Republicans "would have voted to impeach him in a heartbeat with a fraction of the evidence".
Speaking on "Fox News Sunday", Kennedy dodged a question by Chris Wallace on whether Trump was asking Ukraine to investigate corruption or to investigate former Vice President Joe Biden, and instead called out Pelosi for politicizing the impeachment process.