The mother of five has been blocked from leaving Pakistan after her release sparked protests among Islamist hard-liners.
For now, the Christian woman is "hiding in a secret location" but "the good news is that she was able to meet her husband after ten years", the activist said.
During the telephonic conversation, the two foreign ministers discussed the issue of Asia Bibi among other issues.
After pointing out that economic prosperity is linked to respect for the rule of law, they added: "Therefore, we urge in the strongest possible terms the Government of Pakistan to guarantee safe passage for Asia, her family, and any of those under threat due to their part in the decision to acquit her, to any country that accepts them".
Fawad Chaudhry said the images misidentifying Aasia prompted death threats to a lawmaker in one photograph, Fazal Khan from the Pakistan Tehreek-i-Insaf.
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Since her release, Bibi and her family have faced threats and her husband has pleaded with countries in the West to relocate them. Insulting Islam is punishable by death in Pakistan, and the mere rumor of blasphemy can lead to lynchings by mobs.
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Her husband, Ashiq Masih, has said the family is in great danger in Pakistan and has pleaded for asylum in the UK, US or Canada.
The BBC Urdu's report that she had been taken to another country created a lot of confusion and the Foreign Office had to issue a clarification that Bibi was in the country.
TLP supporters closed roads in major cities in Pakistan during three days of demonstrations against Bibi's acquittal at the end of last month. "I am requesting the Prime Minister of the UK help us, and as far as possible grant us freedom", he said in a video message, which also appealed to the United States and Canada.
Pakistan's anti-blasphemy law was established in the British colonial era to avoid religious clashes. The freeing of Bibi has also been highly supported by Christian minority organisations such as International Christian Concern, Open Doors, and Aid to the Church in Need (ACN) that are committed to representing Christians like Bibi facing oppression.
More than 1,300 people have been charged in the last 30 years and many of them have been murdered before their trial is even complete.
Former Foreign Secretary Boris Johnson was reported in the Daily Mail as saying "we can not allow the threat of violence to deter us from doing the right thing".
During a candle-lit vigil in London earlier this week, Wilson Chowdhry of the British Pakistani Christian Association, warned that Britain appeared to be ignoring the plight of Asia Bibi, and this risked hitting its "vaunted and lauded position as a bastion for refuge for the oppressed".