President Donald Trump has bashed one of the loudest neoconservative 'Never Trumpers', Bill Kristol, seizing on news that Kristol's anti-Trump Weekly Standard magazine is folding.

'The pathetic and dishonest Weekly Standard, run by failed prognosticator Bill Kristol (who, like many others, never had a clue), is flat broke and out of business. Too bad. May it rest in peace!' Trump tweeted on Saturday morning.

It follows an announcement on Friday that the Weekly Standard, which Kristol co-founded in 1995, will be ceasing publication.

Kristol, an avid Twitter user, responded to Trump's tweet simply: '@ me next time'.

Neoconservative 'Never Trumper' Bill Kristol (above) co-founded the Weekly Standard in 1995. On Friday the magazine announced that it is ceasing publication

In April 2016, Kristol's Weekly Standard called the prospect of a Trump presidency 'unthinkable'. The neocon magazine perpetually attacked Trump on foreign policy

Trump's attack on Kristol came amid multiple tweets trashing his critics in the press.

'Never in the history of our Country has the “press” been more dishonest than it is today,' he tweeted earlier in the day.

'Stories that should be good, are bad. Stories that should be bad, are horrible. Many stories, like with the REAL story on Russia, Clinton & the DNC, seldom get reported. Too bad!'

A later tweet referring to fired FBI agent Peter Strzok, who was lead investigator for Robert Mueller, read: 'Wow, 19,000 Texts between Lisa Page and her lover, Peter S of the FBI, in charge of the Russia Hoax, were just reported as being wiped clean and gone. Such a big story that will never be covered by the Fake News. Witch Hunt!'

Weekly Standard parent firm Clarity Media, led by billionaire Philip Anschutz, said on Friday the magazine's last edition would be December 17.

Clarity chief executive Ryan McKibben said the news magazine 'has been hampered by many of the same challenges that countless other magazines and newspapers across the country have been wrestling with,' and had seen double-digit declines in circulation in recent years.

Trump, seen on Wednesday, called Kristol a 'failed prognosticator' and celebrated the downfall of Kristol's neocon magazine. It came amid several tweets bashing Trump's media critics

'For more than 20 years The Weekly Standard has provided a valued and important perspective on political, literary and cultural issues of the day,' said McKibben.

'The magazine has been home to some of the industry's most dedicated and talented staff and I thank them for their hard work and contributions, not just to the publication, but the field of journalism.'

The magazine was founded by writers Kristol and Fred Barnes, who remain a part of the editorial team.

Kristol tweeted on Friday: 'All good things come to an end. And so, after 23 years, does The Weekly Standard... We worked hard to put out a quality magazine, and we had a good time doing so. And we have much more to do.'

The magazine strongly supported the policies of president George W. Bush during his two terms in office, but has opposed Trump, notably on issues of tariffs and trade.

A recent editorial harshly criticized Trump as well as the Republicans who have gone along with the president in the face of an investigation linking him to potential criminal acts.

'It is a commonplace, in the Trump era, to say that the old criteria of decency and honor no longer appear to apply,' the magazine said in its December 10 editorial.

'The president's mendacity is so aggressive, his malfeasance so common, that his everyday behavior no longer surprises and these days rarely elicits condemnation from other Republicans.'

Founded under News Corp, The Weekly Standard was acquired in 2009 by Clarity, which also owns the Washington Examiner, Colorado Springs Gazette and Colorado Politics magazine.