The 51-year-old woman had been on the death row since November 2010 after she was convicted of committing blasphemy during an argument with two Muslim women at a village in the Sheikhupura district of Punjab.
While Canadian Prime Minister Justin Trudeau said earlier this week that his government was in talks to grant asylum to Ms. Bibi, who was acquitted of blasphemy charges by the court after almost eight years on death row, there has been growing pressure on the U.K.to also offer asylum.
"We are in discussions with the Pakistani government", Trudeau said in an interview with AFP in Paris, where he was attending a peace conference organised by French President Emmanuel Macron.More news: Last-ditch bid to extend My Health opt-out period
The lawyer, Saiful Mulook, cited death threats in fleeing to the Netherlands soon after the Pakistani Supreme Court decision on October 31 acquitting Asia Bibi of blasphemy.
Bibi is now hiding at an undisclosed "safe place".
Dr Faisal tweeted, "FM Qureshi said that Asia Bibi is our national and Pakistan fully respects her legal rights".
Hard-line Islamists in Pakistan have blocked streets and called for the killing of several people connected with the Bibi case, including the judges who acquitted her.More news: Ebola death toll in DR Congo tops 200
On Tuesday, the ultra-Islamist Tehreek-e-Labaik Pakistan (TLP) party that led the protests said it strictly opposed her release and any permission for her to go overseas.
Last week, Canada urged Pakistan to ensure Bibi's well-being and Foreign Minister Chrystia Freeland said the government was "extremely engaged in this issue".
The Daily Telegraph newspaper, which also quoted Mr. Johnson's letter to the Home Secretary, reported earlier this week that Britain had not offered asylum to Ms. Bibi and her family because of fears it would prompt "unrest" in the United Kingdom and attacks on British Embassies.More news: Rob Kardashian Files to Lower Child Support Payments to Blac Chyna