Local reports quoted unnamed sources as saying that the visiting US Under-Secretary of State also asked his interlocutors to trim India's consulate in Jalalabad, which Pakistan sees as a distraction in the military campaign against Muslim extremists on the Afghan border.
Mr Burns told a news conference after discussions with Prime Minister Manmohan Singh that the 'pace, scope and character' of the India-Pakistan dialogue, suspended since the Mumbai terror attacks, be decided by the leaders of the two countries.
'The US has always welcomed dialogue between India and Pakistan. But it is also obvious that pace, scope and character of that dialogue is something Indian and Pakistani leaders have to decide. And how and when to approach that dialogue is also something for them to decide,' he said.
Mr Burns, the highest ranking US official to visit India after the recent elections, handed over a letter from President Barack Obama to Dr Singh but declined to disclose its contents.
In reply to a question on Kashmir, he said 'It remains our view that resolution of the Kashmir issue has to take into account wishes of Kashmiri people.'
On Mumbai terror attacks, the US official said Pakistan had a special responsibility to bring the perpetrators to justice and take 'concrete steps' to ensure there is 'no repeat' of it. United News of India quoted unnamed sources as saying that the US had asked India to 'close or prune down' its consulate in Jalalabad in Afghanistan following allegations by Pakistan that it was 'creating trouble' in the border areas of NWFP and Balochistan.
UNI said Pakistan had alleged that the Indian consulates in Jalalabad and Kandahar were 'fomenting trouble' in NWFP and Balochistan bordering Afghanistan by providing financial and material support to fugitives in the two border provinces.
'Pakistan, however, has not supported its allegations with evidence,' UNI said. The sources said besides asking India to resume talks with Pakistan, the US was also trying to convey to Indian authorities its views on closing or pruning the Indian Consulate in Jalalabad.
Mr Burns made his comments on Kashmir a day after Hurriyat Conference chief Mirwaiz Umar Farooq proposed a five-point Confidence Building Measures (CBMs) to push forward a process to resolve the Kashmir issue.
He impressed upon the Government of India to take immediate steps to make the atmosphere conducive on the ground.
The Mirwaiz said no process of peace and reconciliation could be possible unless 'draconian' laws like Armed Forces Special Powers Acts and Disturbed Areas Act were withdrawn and demilitarisation started. 'Demilitarisation should start step-by-step,' he said.
He suggested a mechanism be put in place that would help remove hurdles between different parties to this conflict, to enhance mutual partnership in tourism, business and other areas.
'Free movement and free trade within different parts of Jammu and Kashmir state should be started as a confidence-building measure,' said the cleric, under house arrest for 11 days now.
A response was visible to his petition. Visiting Jammu and Kashmir against the backdrop of heightened tension over the rape and murder of two Kashmiri women in Shopian, Home Minister Chidambaram on Thursday said a strategy should be worked out for 'gradual substitution' of federal paramilitary forces by the state police for security and law and order duties.
Mr Chidambaram asked the state government and the security agencies, including the army, to 'sit together (and) work out a strategy for gradual substitution of the Central Reserve Police Force (CRPF) by the local police in the essential duties that should ordinarily be performed by the state police,' reports said.
Speaking at the Unified Command Headquarters meeting, chaired jointly by him and Chief Minister Omar Abdullah, the home minister also made it clear that the field officers and soldiers should not transgress their code of conduct while performing duties.
Mr Chidambaram said 'The Centre is solidly behind the state government in its endeavour to create a stable and secure environment in the state that will be the pre-requisite for development.'
Mr Chidambaram, who arrived in Srinagar on Thursday, reviewed the security situation. The Valley has been witnessing protests over the rape and murder of two women in Shopian, 50 km from Srinagar.