Tory leadership frontrunner Boris Johnson has failed to rule out Brexit.
Mr Johnson said he was "not attracted" to the measure, saying he wanted to deliver Britain's EU exit as "proud representative democracy".
But it is pointedly warned that it was essential.
"I think our colleagues are really starting to come together," he said at a digital hustington hosted by the party. "They are thinking about this in a very mature way and I am not attracted to archaic devices like proroguing.
"Let's get this thing done as a proud representative of the country," said the United States, "that question has a very clear answer.
He also rejected the idea of breaking the deadlines for Brexit, suggesting they did not have the solution to the impasse.
"I think we can get this thing done with a desperate expedient," he said. "I am not able to believe that parliament can leave the problem that the parliament has helped to create.
"Perhaps more sittings of parliament is not what we want."
Mr Johnson said he had confidence that a deal could be passed by MPs without having to choose between no-deal or another extension.
"I think the first thing is to recognize that politics has changed since March 29," he said. "I think that we are facing, not just the Tory Party, but we are facing an existential threat.
"We're going to get it done and we need to move forward and that's why I think they will want to get out of here.
"And when that election comes to an end, I must remember that I think Corbyn for six."
Jeremy Hunt, meanwhile, dismissed a key aspect of his rival Brexit strategy.
Both candidates have a confidence in the future, but have not ruled out pursuing a no-deal exit.
Mr Johnson has suggested that an obscure piece of international trade law, called the General Agreement on Tariffs and Trade (GATT), could be employed in such a scenario, in order to prevent UK firms having to pay tariffs. US.
Mr Hunt, the current foreign secretary, said the suggestion that this was a viable option had to be put to bed.
"I think we've got to knock this thing out," he told the event. "You can only get an agreement to make tariffs if both sides agree to that."
Mr Hunt added: "So there is a no-deal road that would allow us to take advantage of GATT 24."
When it was pointed out to him, Mr. Hunt responded, "I'm not going to try and get drawn into those kinds of comments. that someone is doing something deliberately.
"And I just do not think we should get into that discussion but it's factually the case that you need both sides to agree to Article 24 of GATT."
The two contenders will face more hustings around the country over the next few weeks.
A winner in the contest will be announced on July 23, with the victor expected to be installed in Downing Street the following day.