House Republican Leader Kevin McCarthy on Thursday demanded Nancy Pelosi suspend the Democrats' impeachment inquiry into Donald Trump until Congress can agree on 'transparent and equitable rules' in the process - and was dismissed almost instantly by the Speaker.

His offense move comes as some Republican lawmakers have been grumbling that the White House has not had a concise, planned response to the Democrats' move.

'I am writing to request you suspend all efforts surrounding your 'impeachment inquiry' until transparent and equitable rules and procedures are established to govern the inquiry,' McCarthy, a loyal Trump ally and prominent defender of the president, wrote.

Pelosi responded with a letter of her own, pointing out she has the power to launch an investigation without a vote from the full House.

House Republican Leader Kevin McCarthy demanded Speaker Nancy Pelosi suspend the Democrats' impeachment inquiry into Donald Trump

Speaker Nancy Pelosi has defended her handling of the impeachment process

McCarthy did not suggest what rules should be in place for the impeachment process but accused the speaker of being unfair to President Trump.

Trump gave McCarthy's move his seal of approval and endorsed him for speaker if Republicans win back the House in the 2020 election.

'Leader McCarthy, we look forward to you soon becoming Speaker of the House. The Do Nothing Dems don't have a chance!,' he wrote on Twitter with a retweet of McCarthy's letter to the speaker.

McCarthy outlined 10 questions he asked Pelosi to answer about the impeachment process, including whether the full House would vote on the inquiry, if Republicans would be able to subpoena witnesses during the inquiry, to what extend Trump's attorneys would be involved in questioning witnesses, and who was leading the Democrats' inquiry - Judiciary Committee Chairman Jerry Nadler or Intelligence Committee Chairman Adam Schiff.

Traditionally impeachment inquiries have gone to the Judiciary Committee but Schiff has taken the lead thus far in the process.

McCarthy argued if she said no to his requests Pelosi 'would be denying the President the bare minimum rights granted to his predecessors.'

Pelosi responded in a letter of her own.

'The existing rules of the House provide House Committees with full authority to conduct investigations for all matters under their jurisdiction, including impeachment investigations. There is no requirement under the Constitution, under House Rules, or House precedent that the whole House vote before proceeding with an impeachment inquiry,' she wrote to McCarthy later Thursday afternoon.

She also got it another shot at President Trump in her response.

'As you know, our Founders were specifically intent on ensuring that foreign entities did not undermine the integrity of our elections. I received your letter this morning shortly after the world witnessed President Trump on national television asking yet another foreign power to interfere in the upcoming 2020 elections,' she noted.

Trump on Thursday said China should open an investigation into former Vice President Joe Biden and his son - seeking the aid of a foreign power against his political rival: a move similar to the one that prompted Pelosi to launch the impeachment inquiry into him.

It was the president's request of the Ukrainian president to look into the Hunter Biden's role on a Ukrainian gas company during Biden's time as vice president that led to the impeachment inquiry.

And McCarthy struggled with his defense of Trump in an interview with CBS '60 Minutes' that aired Sunday.

The GOP House leader tried to echo the president's accusations against House Intelligence Committee chairman Adam Schiff when he accused interview Scott Pelley of adding a word to the transcript of Trump's call with Ukrainian President Volodymyr Selensky.

But McCarthy turned out to be wrong.

'What do you make of this exchange?' Pelley asked. 'President Zelensky says, 'We are almost ready to buy more Javelins from the United States for defense purposes.' And President Trump replies, 'I would like you to do us a favor though.'

'You just added another word,' McCarthy said.

'No, it's in the transcript,' Pelley replied.

'He said, 'I'd like you to do a favor though?' McCarthy asked.

'Yes, it's in the White House transcript,' Pelley said.

Speaker Pelosi, meanwhile, defended her handling of the impeachment process during a press conference on Capitol Hill on Wednesday.

And she claimed it was Republicans who would be worried about going on-the-record with a vote about launching an impeachment inquiry.

'There's no requirement that there be a Floor vote. That's not anything that is excluded and, by the way, there's some Republicans that are very nervous about our bringing that vote to the Floor,' she said.

President Trump endorsed McCarthy's move

In both the impeachment inquiries of Richard Nixon and Bill Clinton the full House formally voted to start such a procedure.

'We don't have to,' Pelosi told ABC News.

Such a vote would be lawmakers on the record, heading into an election year, as to whether or not they support the impeachment inquiry.

That could put some Republicans in a politically tough spot as some have grumbled over the White House's handling of the inquiry and others worry if there are more bombshells to come from the president.

'Who knows what playbook they are on,' one GOP lawmaker told The Hill newspaper of the White House response. '[Trump's] pulling it out of his a** as he goes along.'

Other Republicans are not as worried.

Another GOP lawmaker told The Hill the party doesn't 'yet have a coherent response. But I think this is currently like every other Trump 'scandal' — it might be embarrassing but it isn't illegal [or] impeachment worthy.'

McCarthy's office has been emailing guidance and talking points to Republican lawmakers to push back against the Democrats' inquiry as no formal 'war room' has yet been established inside the White House.

Trump needs to hold onto Republican support in Congress.

If the impeachment inquiry reaches the trial level in the Senate, the president cannot lose more than 20 Republicans senators if all Democrats vote in favor of impeachment.