Democratic leaders of the impeachment inquiry against Donald Trump are gearing up for an epic tug-of-war with the White House over their desire to call the former national security adviser John Bolton to testify.

Bolton, who was ousted by Trump in September, is seen by Democrats as a key witness who could prove critical in nailing the president for corruptly leaning on Ukraine to help in his re-election campaign.

The former national security adviser is reported to have expressed deep misgivings about Trump’s attempts to cajole Ukraine into investigating Joe Biden, a leading Democratic presidential candidate and potential rival.

Adam Schiff, the chair of the House intelligence committee who is spearheading the impeachment inquiry, said on Sunday the spotlight was now falling squarely on Bolton.

Speaking on ABC’s This Week, he accused the White House of obstructing proceedings by attempting to block the testimony of current and former officials, adding: “My guess is they are going to fight us having John Bolton in.”

He has a wealth of information and we do want him to come in and testify Adam Schiff

Schiff described Bolton as a “very important witness … He has a wealth of information and we do want him to come in and testify.”

Schiff pointed to the previous testimony of a former aide to Bolton, Fiona Hill. She told the impeachment inquiry her boss had been so alarmed by efforts by the president’s personal lawyer Rudy Giuliani and others to run a rogue foreign policy in Ukraine, designed to dig up dirt against Biden, that Bolton had instructed Hill to alert White House lawyers.

“I am not part of whatever drug deal” was being cooked up, Bolton is reported to have said. According to Hill, he also attacked Giuliani as “a hand grenade who’s going to blow everybody up”.

By swinging the focus on to Bolton, Schiff indicated that Democratic leaders have no intention of allowing the patriotic glow around the killing of the Islamic State leader Abu Bakr al-Baghdadi to knock them off course in their pursuit of Trump.

Schiff implied that any attempt to block Bolton’s appearance before closed-door impeaching hearings would merely delay the start of open public proceedings in the impeachment process – a key demand of the White House and Republicans.

Bolton’s former deputy, Charles Kupperman, filed a lawsuit on Friday asking a judge to determine if he should comply with a subpoena to testify before the House committees as scheduled on Monday. The move was widely seen as a delaying manoeuvre.

If Trump had been hoping that the successful mission to take out Baghdadi would deflect public attention from the gathering impeachment storm and on to a rare foreign policy victory, he would not have been satisfied for long. Even amid a rash of positive comment about the raid on the Sunday political shows, discussion soon reverted to Trump’s troubles.

Vice-President Mike Pence was confronted with a question about impeachment from Chris Wallace on Fox News Sunday. He sought to present the image of Trump as commander-in-chief of US forces pulling off a dangerous mission in Syria as a counterpoint to his beleaguered domestic position.

What the American people have seen in the last 12 hours … is that President Trump has never stopped fighting Mike Pence

“Democrats have been pursuing impeachment by and large for the past three years,” Pence said. “What the American people have seen in the last 12 hours … is that President Trump has never stopped fighting to keep the promises we made in the election in 2016.”

Pence went on to insist that “there was no quid pro quo – the president did nothing wrong”. In fact, devastating evidence has emerged through the impeachment hearings that Trump used the leverage of a Washington summit meeting and almost $400m of military aide to Ukraine to force Kyiv into investigating Biden and other political opponents.

Among the damning evidence is a statement from Trump’s own current chief of staff, Mick Mulvaney, who earlier this month confirmed that there had been a quid pro quo, with military aid withheld. Hours later he tried to retract the statement.

Eric Swalwell, a Democratic member of the House intelligence committee, told Fox News Sunday the Isis raid would have no impact on the impeachment proceedings.

Adam Schiff speaks to the press as he leaves hearings in the Capitol on Saturday. Photograph: Siphiwe Sibeko/Reuters

“We still expect the president to carry out his duties and we are going to continue to hold him to account,” he said. “This can be compartmentalized. We are not concerned about what he did with this Isis raid, we are concerned with the extortion scheme that it looks like he led with the Ukrainians.”

Before news of the Baghdadi raid broke on Saturday night, another of Trump’s former top aides, John Kelly, further added to his travails by saying he had warned the president about the danger of impeachment.

Speaking at an event staged by the conservative Washington Examiner, the former White House chief of staff said that when he left the post he had advised Trump: “Whatever you do, don’t hire a ‘yes man’ – someone who won’t tell you the truth.”

Kelly added that he had given that counsel “because if you do, I believe you will be impeached”.

Trump disputed the claim, lashing back at Kelly in a statement to CNN that “John Kelly never said that … If he would have said that I would have thrown him out of the office.”

A statement from the White House press secretary, Stephanie Grisham, attracted widespread ridicule.

“I worked with John Kelly,” Grisham said, “and he was totally unequipped to handle the genius of our great president.”.