Qureshi said External Affairs Minister Sushma Swaraj sent a letter on Sunday to congratulate Prime Minister Imran Khan and mentioned about talks to resolve issues.
Khan stressed on taking austerity measures, working on tax reforms instead of taking loans, rooting out corruption.
The newly-announced cabinet is expected to take oath on Monday at the President's House.
Khan's government will be the third consecutive democratic government in Pakistan since 2008.
The newly-elected National Assembly, the lower house of Parliament, is meeting to elect the prime minister.
The government and people of Pakistan extend their 'heartfelt condolences' to Vajpayee's family and to the government and people of India, the spokesman said.
The relations between Pakistan and the US nosedived this January after US President Donald Trump accused Islamabad of giving nothing to Washington but "lies and deceit" and providing "safe haven" to terrorists.
Russia has over the past three years provided four Mi-35M combat and cargo helicopters to Pakistan and the militaries of the two countries also held joint drills codenamed 'Friendship'.
Earlier on July 30, Khan, 65, had expressed his desire to take the oath of prime minister on August 11, as his party announced that it had acquired enough seats in the lower house through coalition talks to form a majority government.
PM Modi telephoned Imran Khan to congratulate him on his party's victory in the general elections
PTI leader Naeenul Haq told media on Saturday night that consultations are on to complete the number game.
Jailed former prime minister Nawaz Sharif's Pakistan Muslim League-Nawaz with 64 and former president Asif Ali Zardari's Pakistan Peoples Party with 43 seats are placed at number two and three respectively, the Election Commission of Pakistan said.
PTI spokesman Fawad Chaudhry said that they have the required numbers to form government.
A single party will need at least 137 of the directly elected seats to be able to form the government on its own.
Before the elections, concerns have been raised in the country over the participation of hardline Islamist groups in large numbers.
Counting has begun for the election which will be the second democratic transition of power in the nation's 70-year history.
Decision will be taken in second democratic transition of power in the nation's 70-year chequered history.
Sharif, the PML-N prime ministerial candidate, said that Pakistan cannot become a great nation by voting leaders like Imran Khan who have made false promises to "our nation".
The EU too urged Pak to ensure "safe and secure conditions" for the polls.
The court also refused to suspend the conviction in the case until the appeals were decided.