The message was conveyed by her husband, Ashiq Bibi, who has travelled to the UK to highlight the plight of his wife.
Speaking through an interpreter, Mr Bibi told Premier: "She told [me] that the community must remember her in their prayers because this is an international country... [I] need international pressure for the release of Asia Bibi."
Mr Bibi said Asia's incarceration since 2009 has spelled nine years of "suffering" for the whole family.
He went on to say: "She always has said that Jesus is her life and she is living in the name of Jesus, and [trusting] that Jesus will help her."
Asia Bibi was sentenced to death for blasphemy in 2010 after being accused of insulting the Islamic prophet Muhammad, in a case which has generate huge controversy in Pakistan.
Supporters say there is no truth in the allegation, which was made five days after Asia caused offence by using a water bowl intended solely for Muslims. The subsequent legal battle has led to protests and assassinations in the south Asian nation.
Ashiq added: "We are suffering without Asia because she is the mother, she is the wife. As the husband, I am missing Asia and the daughters are also missing Asia."
Ashiq and Asia's daughter Eisham have been travelling across the UK attending talks - organised by the Catholic charity Aid to the Church in Need - to highlight their plight.
(from left to right: Premier's Alex Williams, Ashiq Bibi and Eisham Bibi)
It is as the Supreme Court in Pakistan is due to rule on an appeal against Asia's death sentence. An announcement on Monday this week was postponed - without a reason being given.
Speaking via a translator, Eisham told Premier: "[Eisham is] praying that her mother is with her as soon as possible and she is also requesting that you [Premier audiences] also pray for their family and especially for Asia.
"The family of Asia Bibi is always under threat and when Asia Bibi would be [sic] released from the jail she will never, ever be living in Pakistan [again]."
#Thursdaythoughts Have a listen to our National Director Neville Kyrke- Smith speak to @BBCShropshire about the trial of Asia Bibi and how ACN have been supporting her family during this time > Skip forward to 1 hour 8 minutes https://t.co/pdSF1tWEJd #AsiaBibi #Pakistan @acn_uk pic.twitter.com/L8Usn7q72k— ACN Scotland (@ACN_Scotland) October 11, 2018
It has been claimed the case of Asia Bibi is just one example of how blasphemy laws in Pakistan have been misused to settle personal vendettas.
Fr Emmanuel Yousaf from the Catholic Church in Pakistan told Premier that minority groups - including Christians - are particularly vulnerable to such abuse of legislation.
He said: "Lesser citizens of Pakistan have been very, very badly disturbed by this.
"We are asking the government over there to take measures for some procedural change... so that this law is not misused by anybody."
Click here to listen to Premier's Alex Williams speaking with Ashiq Bibi:
Click here to listen to Premier's Alex Williams speaking with Eisham Bibi:
Click here to listen to Premier's Alex Williams speaking with Fr Emmanuel Yousaf at the Pakistan Catholic Bishops' Conference:
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