Tory leadership rivals Boris Johnson and Jeremy Hunt have unveiled pledges on immigration and education.
Frontrunner Mr Johnson has promised to deliver an Australian-style points-based immigration system if he becomes prime minister.
And Foreign Secretary Mr Hunt said he would cancel the tuition fee debts of young entrepreneurs who start businesses and employ people.
The winner of the contest will take over from Theresa May on 24 July.
In the Conservative Party digital hustings, broadcast on the party’s Facebook page and on Twitter on Wednesday evening, Mr Johnson said he was “open to talent, open to immigration” but he said it “should be controlled”.
He called for an Australian-style-points-based system, considering factors including whether an immigrant has a firm job offer before arrival and their ability to speak English.
Mr Johnson said he would also block the ability to claim benefits immediately when someone arrives in the UK.
“We must be much more open to high-skilled immigration such as scientists, but we must also assure the public that, as we leave the EU, we have control over the number of unskilled immigrants coming into the country,” he said.
This would restore public faith and democratic control in the immigration system, while being “tougher on those who abuse our hospitality”, he added.
The Immigration and Social Security Co-ordination (EU Withdrawal) Bill is currently at report stage and contains plans to end the existing automatic preference for EU citizens.
However, the Bill does not set out what the new immigration system will look like from 2021, and a consultation to shape this is not due to report back to Parliament until the end of this year.
‘Turbo-charge our economy’
Under Mr Hunt’s new proposal, anyone who creates a new business which employs more than 10 people for five years would have their university tuition fee debts written off.
Mr Hunt, who has stressed his background as an entrepreneur, said he wanted to give young people the confidence to go into business for themselves.
“If we are to turbo-charge our economy and take advantage of Brexit, we need to back the young entrepreneurs who take risks and create jobs,” he said.
“I started my own business, I still use the lessons that experience taught me – focus, drive and the art of negotiation – every single day.
“I want more young people to have the confidence to take the decision to start their own business, so we create wealth and start thriving as a country again.”
Meanwhile, Mr Hunt spoke for the first time about the death of his sister in a “terrible accident” when he was only two years old.
“I was too young to ever remember it but I do know it affected my parents,” he told ITV’s Peston.
“I wouldn’t claim this is something that had a big emotional affect on me personally.”
Each candidate is vying for the votes of the 160,000 or so Conservative Party members who will vote for the next party leader and therefore prime minister.
The rivals used the digital hustings to set out some of their plans:
Mr Hunt said if the UK gets to October without the prospect of deal, “we will leave without a deal”.
Mr Johnson also repeated his pledge to get the UK out of the EU on 31 October, but he thinks the chances of a no-deal Brexit happening are a “million to one”.
On an election
Mr Hunt said it was essential the Conservatives had delivered Brexit before a general election, otherwise the party “will be thrashed”.
Asked about proroguing Parliament, Mr Johnson said: “It would be absolutely crazy for any of us to think of going to the country and calling a general election before we get Brexit done.”
When pushed, he added: “I’m not attracted to archaic devices like proroguing.”
On trade rules
Mr Hunt dismissed rival Mr Johnson’s claims that a mechanism known as Gatt 24 could be used to prevent tariffs if there was a no-deal Brexit.
He said: “I think we’ve got to knock this Gatt 24 thing on the head. You can only get an agreement not to introduce tariffs if both sides agree to that.”
On EU citizens’ rights
Mr Hunt said he would give full citizens’ rights to the three million EU nationals living in the UK, even if the UK left without a deal.
Mr Johnson said he was “absolutely in favour” of protecting the rights of EU citizens in the UK.
The foreign secretary said he would back both the third runway at Heathrow and the HS2 high-speed rail link.
Mr Johnson said it had to be recognised that there was “huge pressure” on the south east, so more infrastructure was needed.
Mr Johnson said the NHS would be “free to everybody at the point of use” under his premiership.
He ruled out a pay-for-access NHS, even as a result of a post-Brexit trade deal with the US.