The Foreign Office said Tillerson conveyed the greetings on behalf of the US government and the American people to the government and people of Pakistan.
He also congratulated Asif for taking charge as Foreign Minister of Pakistan and expressed his desire to work with him towards achieving common objectives.
Asif said the call from Tillerson on the 70th anniversary of Pakistan's Independence Day was an apt reminder of the long history of relations between the two countries.
Noting that he would strive in his new capacity to strengthen partnership with the US, Asif said the current leadership of Pakistan was committed to establishing Pakistan's vital relations with America.
He underscored the need to build a dynamic and diverse relationship underpinned by mutual trust, sincerity and confidence, the statement said.
The Foreign Minister said that Pakistan would benefit the most if peace and stability were achieved in Afghanistan as the success and sustainability of Islamabad's economic reforms depended on peaceful and stable Afghanistan.
Asif emphasised on the political settlement of the conflict in Afghanistan as common objective of Pakistan and the US.
Tillerson also extended an invitation to Asif for a visit the US. Asif also invited Tillerson to visit Pakistan and the the Secretary of State accepted the invitation, the statement said.
Army Chief General Qamar Javed Bajwa today hoisted the largest flag in Pakistan's history at Attari-Wagah border near Lahore to mark the country's 70th Independence Day.
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