Mr Stride, the shadow work and pensions secretary, won 16 votes in the last round of voting, meaning if his supporters go on to support Mr Cleverly too, it would put him within touching distance of the final round.
Meanwhile Robert Jenrick, who has been the frontrunner for most of the race, is expected to secure a slew of senior endorsements ahead of today's vote.
But Tom Tugendhat and Kemi Badenoch's teams insist they have widespread support and the race is "definitely still wide open".
Mr Stride's endorsement came after the shadow home secretary was widely viewed as delivering the speech with the biggest impact at the Conservative party's conference last week.
Mr Stride said: "We must pick a leader who can hit the ground running, take the fight to Labour and make sure that we are ready to win as soon as the opportunity presents itself.
Appeal
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Heading home in the ruins
THOUSANDS of families started to head home to southern Lebanon yesterday on the first day of the Israel-Hezbollah ceasefire. Civilians flooded back into the former war zone.
'If I saw George and John again I would tell them I love them'
SIR Paul McCartney has paid a moving tribute to the two Beatles who are no longer with us.
'Budget has destroyed me. I'd have to put 40p on a pint to cover £28k extra costs'
A BAR owner has warned of a dystopian future where only big chain pubs and restaurants survive because of Labour's crippling Budget and national insurance hikes.
Photographer who shared bond with Kate dies aged 17
TEENAGE photographer Liz Hatton who shared a tender hug with the Princess of Wales last month has died.
Now BBC gives a kicking to stars of women's football
THE SUFFRAGETTES must be turning in their graves at the state of modern British womanhood, or rather its perception by everyone else. Right now, we're holding our breath to see whether the judges of the Supreme Court can actually define a woman.
Wild night out for William and Rolling Stone Ronnie
PRINCE William and Stones legend Ronnie Wood had a wild night out with a difference yesterday - when they met at a conservation awards bash.
AI Fayed abuse probe: Police investigating more than 5 people over enabling claims
A POLICE investigation has been launched into \"more than five people\" who may have helped former Harrods boss Mohamed AI Fayed in his alleged campaign of sexual abuse.
Guardiola: I didn't mean to make light of self-harming
MANCHESTER City manager Pep Guardiola insisted yesterday he did not mean to make light of self-harm issues after a \"flippant\" comment about his facial injuries.
NHS boss denies he 'discouraged' Letby investigation
THE hospital boss in charge when Lucy Letby murdered seven babies in its neonatal unit yesterday denied he had tried to avoid a criminal investigation.
Davina: My memory's coming back
DAVINA McCall yesterday told how her post-surgery short-term memory loss is easing daily as she recovers at home from her brain operation.
