Such an assurance was given by Pakistan Foreign Minister Shah Mehmood Qureshi during a phone call on Monday, Bolton said in a tweet on a day when Foreign Secretary Vijay Gokhale called on US Secretary of State Mike Pompeo here.
"Spoke with Pakistani FM Qureshi to encourage meaningful steps against JeM and other terrorist groups operating from Pakistan," Bolton said. "The FM assured me that Pakistan would deal firmly with all terrorists and will continue steps to de-escalate tensions with India," he tweeted. Tensions flared up between India and Pakistan after a suicide bomber of Pakistan-based Jaish-e-Muhammed (JeM) killed 40 CRPF personnel in Kashmir's Pulwama district on February 14.
In Islamabad, Pakistan's Foreign Office said the purpose of Qureshi's call was to provide Bolton Pakistan's perspective on the "recent regional developments."
Qureshi said that Pakistan Prime Minister Imran Khan decided to hand over the Indian Air Force pilot as a gesture of goodwill towards India. Pakistan wished peace and stability in the region, he was quoted as telling the US National Security Adviser.
The foreign minister also informed Bolton that Pakistan's High Commissioner to India has returned to Delhi after consultations.
During talks between Gokhale and Pompeo, the United States continued to maintain pressure on Pakistan, according to a readout of the meeting issued by the State Department.
"Secretary Pompeo and Foreign Secretary Gokhale discussed the importance of bringing those responsible for the (Pulwama) attack to justice and the urgency of Pakistan taking meaningful action against terrorist groups operating on its soil," State Department Deputy Spokesperson Robert Palladino said.
Pompeo affirmed that the United States stands with the people and government of India in the fight against terrorism, he said.
"They noted the strength of our partnership and discussed ways to further enhance cooperation, including on counter-terrorism," Palladino said.
Secretary Gokhale conveyed India's appreciation to the US Government and to Secretary Pompeo personally for the firm support that India received from the US in the aftermath of the terrorist attack in Pulwama, the Ministry of External Affairs said in a statement on the meeting.
Secretary Pompeo expressed his understanding of India's concerns regarding cross-border terrorism, it said.
"They agreed that Pakistan needs to take concerted action to dismantle the terrorist infrastructure and to deny safe haven to all terrorist groups in its territory. They also agreed that those who support or abet terrorism in any form should be held accountable," the statement said.
Amid mounting outrage in India over the Pulwama terror attack, the Indian Air Force carried out a counter-terror operation, hitting the biggest JeM training camp in Balakot, deep inside Pakistan on February 26.
The next day, Pakistan Air Force retaliated and downed a MiG-21 in an aerial combat and captured Indian pilot, who was handed over to India on March 1.
The escalation of tensions between the two nuclear-armed neighbours prompted the major powers to intervene and urged both Pakistan and India to de-escate.
Secretary of State Pompeo was directly in touch with the leadership of both India and Pakistan to de-escalate tensions. The international community also mounted pressure on Islamabad to act against the terror groups operating from the country and stop providing safe havens to them.