The request by Asia Bibi's husband Ashiq Masih came a day after he criticised a government deal with hardline Islamists that left her in legal limbo, and called on authorities to protect her.
Bibi - who had been on death row since 2010 on blasphemy charges - was acquitted by the Supreme Court Wednesday, triggering large street protests by ultra-conservative Islamists who paralysed Pakistan for three days, blocking roads and disrupting traffic.
The government reached a deal Friday to end the protests by agreeing to a travel ban preventing Bibi from leaving the country, and saying it would not object to hardline movements appealing the verdict.
An appeal has now been filed with the court against Bibi's release. Masih criticised the government deal, saying it was "wrong".
"I request President Donald Trump to help us to leave (the country), and I request the prime minister of the UK to do their level best to help us, to grant us freedom," said Masih, in a video message, seen by AFP, also requesting help from the Canadian prime minister.
Wilson Chowdhry, of the British Pakistani Christian Association, told AFP that the family was resting its hopes on the US, Britain or Canada to grant them asylum and help them reach a place of safety.
"These nations have the largest Pakistani Christian communities," Chowdhry said, added that Masih also wants asylum for some members of the extended family and those who have helped with his wife's case, one of whom could speak English.
"If Asia Bibi leaves the country, every family member, every person associated to her, will be killed," he said.
Chowdhry said the family's initial relief at Bibi's acquittal has turned into anguish.
"The daughters are weeping. They still haven't seen their mother. The family is totally shattered," he said.
"They absolutely don't know when they will see their mother. Since (the court decision), with the violence and the protests, it is too dangerous for them to see their mother in jail." Blasphemy is a hugely inflammatory charge in Muslim-majority Pakistan, where even unproven allegations of insulting Islam can spark attacks and killings at the hands of vigilante mobs.
Masih Saturday told German Deutsche Welle radio the court had been "very courageous" to acquit his wife, an illiterate mother in her 50s who was accused of blasphemy a decade ago.
"The current situation is very dangerous for us. We have no security and are hiding here and there, frequently changing our location," he told the German radio station, saying he was worried his wife would be attacked in prison.
The case began in June 2009 when Bibi was asked to fetch water while out working in the fields. Muslim women labourers objected, saying that as a non-Muslim, she should not touch the water bowl, and reportedly a fight erupted.
A local imam then claimed Bibi insulted the Prophet Mohammed - a charge she has consistently denied.
Masih demanded the government reinforce Bibi's protection in prison, worrying that she may be attacked. He cited the case of two Christian men who were shot dead after a court acquitted them in another blasphemy case.