The intrusion by US forces caused embarrassment to Pakistan's political and military establishments and the country has been demanding answers to disturbing questions raised by it, the Dawn newspaper quoted a source in the presidency as saying.
Zardari will soon start contacting the leadership of major political parties and apprise them of the situation and try to take them on board, the source said.
The President might talk to heads of opposition parties on telephone and he could hold meetings with the leadership of other political parties, particularly the coalition partners of the ruling Pakistan People's Party, the source said.
After two days of protest on the US raid by opposition members, Information Minister Firdous Ashiq Awan came to the Senate or upper house of Parliament yesterday and read out a statement issued earlier by the Foreign Office on Tuesday night.
The opposition parties have described the US operation on Monday as a failure of the civil and military leadership and said the raid was an attack on Pakistan's sovereignty.
They called for reviewing Pakistan's policy on the US-led war against terrorism.
A number of opposition members asked Senate Chairman Farooq H Naek on Monday to call the Prime Minister within 30 minutes to take the House into confidence over the incident.