The Foreign Secretary said he was not giving any ‘commitment’ on dates, while arguing that he was the candidate with the best chance of getting the UK out of the bloc quickly.
The guarded stance came as Mr Hunt and Boris Johnson faced one of their toughest tests, in the form of a grilling from combative BBC interviewer Andrew Neil.
Mr Johnson has insisted he will force through Brexit by October ‘come what may’.
But when Neil demanded to know whether Mr Hunt could pledge that the UK would be out by the end of the year, he replied: ‘I am not going to give these commitments.’
Pressed again, he added: ‘Prime Ministers should only make promises they know they can deliver.’
The clash came with just over a week to go before the contest reaches its dramatic conclusion, with the winner getting the keys to Downing Street.
Jeremy Hunt tonight refused to guarantee Brexit will happen by Christmas – insisting politicians should not make promises they cannot keep
Despite claims most Tory members intended to vote early, MailOnline understands only around half of eligible activists have cast their ballots so far.
Business Secretary Greg Clark today became the latest senior Conservative to signal he will join a mutiny over hard Brexit.
He warned No Deal – which Mr Johnson has said should happen in October if an agreement cannot be struck with the EU – would mean the loss of ‘many thousands’ of jobs.
Mr Johnson (pictured today in London) is the hot favourite in the Tory leadership contest
Jeremy Hunt pictured arriving at BBC studios for the interview with Andrew Neil this afternoon
In an interview with Sky News, Business Secretary Greg Clark today became the latest senior Conservative to signal he will join a mutiny over hard Brexit
He said he would ‘strain every sinew to avoid that’ alongside colleagues.
Boris: I will end prosecution of NI vets
Boris Johnson has pledged to end ‘unfair’ prosecutions of veterans who served in Northern Ireland as part of his push to become the next Prime Minister.
The Tory leadership contender has joined rival Jeremy Hunt in backing a public campaign supporting UK soldiers who served during the Troubles.
A number of veterans are facing inquiries, including Soldier F, who has been charged in relation to the killings of two protesters on Bloody Sunday in Londonderry in 1972.
Mr Johnson, speaking from his campaign headquarters on Thursday, also reportedly promised to appoint a Veterans Minister if he is chosen to lead Britain. He told The Sun: ‘We need to end unfair trials of people who served their Queen and country when no new evidence has been produced, and when the accusations have already been exhaustively questioned in court.
The comments underline the challenge facing Mr Johnson if he tries to follow through on his solemn ‘do or die’ pledge made during the campaign.
Mr Hunt has taken a marginally softer stance by saying he would be willing to delay if a deal was in sight – and admitting that Parliament can probably block No Deal.
Speaking to Sky News today, Mr Clark said: ‘It’s evident that if you have the disruption that comes from a no-deal Brexit there will be people that will lose their jobs,’ he told Sky News.
‘It’s many thousands of jobs. Everyone knows that.’
Mr Clark cited evidence from businesses when challenged that some are claiming the UK could weather an exit on World Trade Organisation terms.
‘I think every person that considers the evidence that companies have given – whether it’s in the automotive sector, whether it’s in the food sector, whether it’s in aerospace, in industries up and down the country – you know if you become less efficient and your ability to trade is impeded, then of course losing your competitiveness means there will be jobs lost,’ he said.
Mr Clark hinted strongly that he will vote against No Deal in Parliament.
‘I will do everything I can in whatever forum,’ he said.
Tension is building in the contest, but Mr Johnson appears to have a commanding lead.
Rudd drops No Deal opposition – paving way to serve in Boris Johnson’s Cabinet
Amber Rudd has appeared to drop her opposition to No Deal Brexit – potentially paving the way to stay in a Boris Johnson Cabinet.
Mr Johnson has insisted if he becomes PM all ministers must be willing to sign up to leaving the bloc by Halloween ‘come what may’.
Work and Pensions Secretary Ms Rudd, who has been backing Jeremy Hunt for Tory leader, has previously been seen as one of the strongest opponents of No Deal.
But in an interview with TalkRadio today she said: ‘Both candidates have said that no deal is part of the armory and the negotiations going forward.
‘And I have accepted that, um, that the situation is that we are leaving by the end of October.
‘But it would be so much better to get a deal.’
A survey for the grassroots ConservativeHome website yesterday found 72 per cent also said they had either backed or planned to back Mr Johnson.
Mr Hunt has admitted he is the underdog in the contest to replace Theresa May, but vowed to fight to the end.
He mounted an all-out assault on Mr Johnson in a TV debate earlier this week as he desperate struggles to overhaul his advantage – mocking him for refusing to answer questions and questioning his ‘do or die’ pledge to force Brexit by the end of October.
However, the attacks do not seem to be making a significant dent in Mr Johnson’s popularity with members.
Mr Johnson was put on notice to expect a legal battle with former prime minister Sir John Major if he tries to suspend Parliament in order to force through a no-deal Brexit.
Former Conservative leader Sir John said it would be ‘utterly and totally unacceptable’ for any British premier to shut down Parliament, and he would seek a judicial review if it happened.
Mr Johnson dismissed Sir John’s ‘very odd’ threat of being dragged through the courts, insisting that Parliament should accept its responsibility to deliver Brexit.
But he has refused to rule out proroguing Parliament to prevent MPs blocking a no-deal exit from the European Union on October 31.
In the ConHome survey, some 72 per cent also said they had either backed or planned to back Mr Johnson – suggesting he is on track for a landslide victory when the result is announced in two weeks’ time
Jeremy Hunt (pictured out running at hustings last night) has admitted he is the underdog in the contest to replace Theresa May, but vowed to fight to the end
How will the next few months of political drama play out?
Today: Leadership contenders put themselves under the microscope in separate TV interviews with the BBC’s Andrew Neil.
July 22: Ballot closes
July 23: The new Tory leader is announced
July 24: Changeover day. Theresa May takes her last PMQs in Commons, before heading to the Palace to quit.
The new Tory leader will follow her in to be asked to form a government.
July 25: Probable Cabinet reshuffle. Parliament is also due to rise today, sending MPs away on their summer holidays.
September 3: Parliament is due to return for two weeks, before the party conference season starts.
October 2: Tory conference wraps up with the new leader’s speech.
October 7: Parliament sits again.
October 31: The UK is due to leave the EU.