Narendra Modi sworn in as India's new PM with Pakistani counterpart Nawaz Sharif looking on

India’s newly elected leader will on Tuesday have an official meeting with his Pakistani counterpart amid cautious optimism on both sides of the border the two leaders can push forward their countries’ vexed and painful relationship.

A day after he was sworn in as India’s 15th prime minister, Narendra Modi will have a 30-minute meeting with Nawaz Sharif, whose decision to come to Delhi and attend the ceremony marked an historic first between the two nations.

The relationship, heavy with the weight of history, is in something of a stalemate as the two terms of India’s Congress-led government ran their course without making much progress. The 2008 attack on Mumbai by Pakistani militants set back any advances that had been made and added to the mutual distrust felt between two nations that have gone to war on four occasions.

Many in India believe the Hindu nationalist Mr Modi, who earlier his month won a landslide election victory, will have more capacity to deal with Pakistan as he will not be vulnerable to attacks from the right. His counterpart, who last year was elected for the third time as premier, is also seen as a nationalist and a religious conservative.

Mr Sharif was one of eight foreign leaders who attended Mr Modi’s beguiling swearing-in ceremony against the backdrop of Delhi’s Rashtrapati Bhavan, the official residence of India’s president. After Mr Modi issued the invitation to Mr Sharif and the other leaders of the nations that make up the South Asian Association for Regional Cooperation, there was intense debate inside Pakistan as to whether or not he should accept.

As it was, Mr Sharif decided the potential benefits outweighed the risks. “This is a chance to reach out to each other. Both governments have a strong mandate,” he said in an interview with India’s NDTV television channel. “Both countries should rid the region of instability and security that has plagued us for decades.”

Nobody thinks India and Pakistan are set to become best friends anytime soon. India believes Pakistan is doing insufficient to control militants and has moved too slowly to bring to justice those responsible for the three-day assault on Mumbai that left more than 160 people dead.

Pakistan, meanwhile, accuses India of refusing to want to address the issue of Kashmir, the Muslim majority territory which both countries claim and over which there have been repeated clashes and bloodshed.

But some believe that Tuesday’s meeting between the two premiers, when they are likely to focus on boosting trade, could provide an opportunity to size each other up.

Neelam Deo, an analyst and director of the Indian Council on Global Relations, said she expected no major breakthrough on Tuesday. “I don’t think there is going to be anything substantial from the first meeting,” she said. “But I do think they will take the measure of each other.”

Mr Sharif took several days before responding to Mr Modi’s invitation to attend Monday’s event and there were many in both countries who thought he should not come. As it was, Monday marked the first time that a leader from either side had attended the swearing-in of a premier from the other country.

Hassan Askari Rizvi, a political scientist based in Lahore, said many in Pakistan believed Mr Modi was someone they could do business with. He said there were still concerns about Mr Modi’s record in Gujarat, where hundreds of Muslims were killed in 2002, and over some of the statements he made about Pakistan during his election campaign.

However, many there remember efforts made by a previous Indian prime minister from Mr Modi’s Bharatiya Janata Party (BJP), Atal Bihari Vajpayee, who in 1999 famously took a bus to Lahore as part of a peace initiative. His counterpart in Pakistan on that visit was Mr Sharif.

“There is a lot of hope that he can help bring change,” said Mr Rizvi. “There is hope that the dialogue between the two countries could start again in a couple of months.”

Taking his oath in Hindu, Mr Modi, 63, the son of a tea salesman who secured the biggest mandate in India for 30 years after a campaign when he pushed a message of growth and development, said he would “maintain the integrity of India”.

In a message posted on the website of the prime minister’s office, Mr Modi said he believed he could work with India’s citizens to create a “glorious future”. “Let us together dream of a strong, developed and inclusive India that actively engages with the global community to strengthen the cause of world peace and development,” he said.

Also taking the oath of office with Mr Modi, in front of an audience that included Bollywood actors, leading industrialists and foreign diplomats, were the 45 ministers who will make up his government.

Among the senior positions, Arun Jaitely will take on defence and finance, Shushma Swaraj is lined up to become India’s foreign minister, while Rajnath Singh, the head of the BJP, will become home minister. Seven women ministers have been named in the cabinet.