During their meeting, both Burns and Jilani, "underscored" that both the countries "look forward to deepening these discussions" during the upcoming Strategic Dialogue Ministerial.
The meeting was held at the Foggy Bottom headquarters of the State Department.
The US diplomat welcomed Jilani in his new role as the Ambassador and noted that "we look forward to continuing our productive working relationship", a State Department statement said.
"Conveying the greetings of the Government and people of Pakistan to Deputy Secretary Burns, Ambassador Jilani exchanged views on the state of play in the bilateral relations which has seen new vigour and momentum after the visit of Prime Minister Nawaz Sharif to Washington in October last year," the Pakistan Embassy said in a statement.
The former foreign secretary, Jilani arrived in Washington in the last week of December and presented copies of his credentials to Natalie Jones, the Acting Chief of Protocol at the State Department on January 2.