Indian Prime Minister Manmohan Singh is expected to make a pitch for India gaining a permanent UN Security Council seat in a speech on Thursday.
Singh says he is keen to listen to Pakistani proposals
Mr Singh is also expected to call for a level playing field in foreign trade in his address to the United Nations General Assembly in New York.
He is in the US on his first major diplomatic trip since taking office.
Mr Singh and Pakistani President Pervez Musharraf are to meet on Friday on the sidelines of the UN meeting.
The two South Asian leaders are among about 100 heads of state and government attending the General Assembly.
The BBC's Urdu service correspondent, Shahzeb Jillani, in New York says that the Pakistani side will be closely following Mr Singh's speech to see whether India talks tough on Pakistan or makes reconciliatory statements to strengthen the ongoing peace process.
'Moment for peace'
President Musharraf told the UN General Assembly on Wednesday that Pakistan was committed to solving its dispute with India over Kashmir.
He said he would tell India's premier in talks on Friday: "This is the moment for peace. We must not let it slip."
Our correspondent says that General Musharraf's UN speech this year was unusual and a clear departure
from Pakistan's annual diplomatic offensive against India over Kashmir.
For the first time in decades, direct attacks on India over human rights
abuses in Kashmir and India's alleged strong-arm tactics to "suppress the
just struggle for Kashmiri self determination" were conspicuously absent
from the general's speech.
Neither was there a mention of UN Security Council resolutions on Kashmir or
an attempt to equate the Israeli occupation to India's policy in Kashmir.
Instead, General Musharraf's emphasis remained on working sincerely to
resolve "all disputes with India peacefully including the Kashmir dispute"
and "giving bilateralism a final chance."
The Indian side reacted in a favourable, but well-guarded tone.
"We are encouraged by the speech," Indian government spokesperson Navtej Sarna told the BBC.
"It has been our consistent position that the two countries should resolve their disputes bilaterally. So, in that sense, it is positive," he added.
In an interview ahead of his General Assembly speech and meeting with President Musharraf, Mr Singh has said he was "very sincere" in wanting better ties with Islamabad.
Mr Singh told The Wall Street Journal newspaper that his meeting with General Musharraf would be "an essay in mutual comprehension".
He said he was interested in hearing from the Pakistani leader "what opportunities he has in mind" for improving relations.
"I am very sincere in... the desire to normalise relations with Pakistan," Mr Singh said.
President Musharraf's meeting with the Indian premier will be the first between the two since Mr Singh's Congress-led coalition government took office in May.
Musharraf hopes for a good relationship with Singh
General Musharraf told the BBC he hoped to develop a good relationship with Mr Singh.
"This is going to be an important meeting. I am going with a very open mind," the president said.
"This first meeting is meant to develop relationships, understandings because I think that is very important as a prerequisite to looking for solutions."
Mr Singh has promised to engage constructively with Pakistan over Kashmir, provided the threat caused by Kashmiri separatists could be kept under control.
India accuses Pakistan of sponsoring an Islamic uprising in its part of Kashmir. Pakistan says it only lends diplomatic backing to an indigenous insurgency against Indian rule.
The two nuclear-armed neighbours have gone to war three times - twice over the disputed region of Kashmir.