At Tuesday's meeting at the State Department, Burns and Jaishankar "affirmed the importance of the US-India strategic partnership," the State department said in a statement
"They agreed that the past several weeks have been challenging," it said in a reference to the month long diplomatic row sparked by the arrest and strip search of Devyani Khobragade, 39, India's then deputy consul-general in New York.
She was asked to return home Jan 10 after India declined to waive her diplomatic immunity to enable her prosecution charges of visa fraud and underpaying her housekeeper even as she was indicted by a grand jury in New York.
Burns and Jaishankar "affirmed that we are both committed to moving forward to resume cooperation on the broad range of bilateral issues before us," the State Department said.
The two also discussed the variety of issues raised by the Ministry of External Affairs via diplomatic note, including alleged issues with the American Embassy School, it said.
Khobragade's lawyer filed a petition in the Manhattan federal court.
Burns conveyed that the US takes "their concerns very seriously and will continue to address them via appropriate diplomatic channels."
Burns and Jaishankar "affirmed our shared commitment to continue joint US-India work on issues such as clean energy and climate change, defence, economic and trade engagement, counterterrorism, and civil nuclear development," the State Department said.
"To that end, they discussed initial preparations for a range of upcoming bilateral meetings and exchanges," it said.
Meanwhile, Khobragade's lawyer Daniel Arshack filed a petition in the Manhattan federal court Tuesday asking the trial judge to throw out the charges against her.