Rishi Sunak and Liz Truss have been accused of “cruelty and immorality” for promising more Rwanda-style deals to remove asylum seekers from the UK, as charities claimed the pair were pandering to party members’ hardline views.

Amnesty International led criticism of immigration plans announced over the weekend by the Tory leadership candidates, saying the “dreadful” pledges would come at “great human and financial cost”.

Other human rights groups, opposition parties and the rightwing Adam Smith Institute thinktank also condemned the proposals on grounds ranging from ethics to the “crippling costs”.

Hostile briefings by the two camps intensified over the weekend as they prepared for a crunch TV debate hosted by the BBC on Monday evening, with ballot papers set to drop through members’ letterboxes in just over a week.

The row about immigration threatened to overshadow their latest announcements, with Sunak pledging to take tougher action against China by banning its network of Confucius Institutes, while Truss announced plans to cut red tape for freeports and create new “investment zones” with fewer planning restrictions.

Both promised to push ahead with the plan to send hundreds of asylum seekers to Rwanda, which stalled last month after an intervention by the European court of human rights.

Sunak said he would do “whatever it takes” to get the Rwanda plan “off the ground and operating at scale” and vowed to pursue more “migration partnerships” with other countries.

In a 10-point plan on immigration, Sunak said he would cap the number of refugees the UK accepted each year, tighten the definition of who qualified to claim asylum, and withhold aid money from countries that refused to take back those whose claims were denied and criminals.

In an article for the Sunday Express, Boris Johnson insisted he had delivered a key pledge to “take back control” of Britain’s borders, but the former chancellor contradicted that assessment.

“We do not have control of our borders,” Sunak said, adding that immigration should be legal, orderly and controlled but “at the moment, it’s none of those things”.

Sunak’s plan to house migrants in cruise ships instead of hotels to save money was criticised by Truss’s campaign, which said the move would be likely to amount to arbitrary detention and a breach of domestic and international law. Pressed in a media interview on whether his proposals would be legal, Sunak did not give clear assurances, instead insisting “no option should be off the table”.

The foreign secretary also said she was “determined to see the Rwanda policy through to full implementation as well as exploring other countries where we can work on similar partnerships”.

She pledged not to “cower” before the European convention on human rights, and to reform Britain’s relationship with the Strasbourg-based court of human rights “so it works better”.

Although she is, unlike Sunak, a Brexit convert who voted remain in the 2016 EU referendum, the foreign secretary is seeking to present herself as the true heir to Johnson who will finish the job of overhauling immigration policy.

Frontline Border Force capacity would be increased by 20% if she became prime minister, Truss promised, allowing more Channel patrols to take place to help curb the number of small boat crossings.

Truss and Sunak were accused by Amnesty International UK of “making promises and policy based on nothing more than what is thought to appeal to some Conservative party members”.

Steve Valdez-Symonds, the charity’s refugee and migrant rights programme director, said it was the same as it had been for the last three years, and added: “It is why our asylum system has collapsed into chaos and backlogs – all at great human and financial cost.”

He said: “It is dreadful that those who aspire to lead are showing no capacity for leadership, which requires focus on what is possible, necessary and lawful.

“Instead, they are setting out on the same dismal course of blaming people fleeing persecution, lawyers and courts for all the ills that our politicians continue to heap upon everyone, rather than taking responsibility for making our asylum system work fairly and efficiently.”

Zehrah Hasan, advocacy director at the Joint Council for the Welfare of Immigrants, also said both politicians were “showing their fierce commitment to cruelty and immorality by trying to abdicate all responsibility for people forced to move to the UK”.

She continued: “They want to expand the hostile environment and ramp up the brutalisation of refugees for political point-scoring. Their plans will only destroy more lives and tear more families apart.”

Concerns were also raised over the value-for-money feasibility of the Rwanda plans, which have cost taxpayers £120m in exchange for up to 200 asylum seekers being relocated.

Emily Fielder, head of communications for the Adam Smith Institute, said it was ineffectual because “in reality, barely any flights to Rwanda will take off, leaving an asylum system continuing to struggle with a huge backlog and crippling costs”.

She added: “Rather than governing by press release, the Conservative party should look towards engaging more constructively with our European partners, introducing safe routes for those fleeing persecution and implementing vital reforms to clear the backlog of legacy asylum cases.”

Yvette Cooper, the shadow home secretary, said it was “dismal” to see Sunak and Truss “competing to extend an unworkable, unethical, unaffordable, high fraud risk Rwanda scheme” that she said would only make trafficking worse.

The Liberal Democrats said both leadership candidates wanted to “throw away more good money after bad” and “should never be trusted again with taxpayers’ money, let alone trusted to treat asylum seekers with decency and respect”.