( CNN ) -- Pakistan 's Prime Minister Nawaz Sharif hailed his first one-on-one meeting Tuesday with India 's newly elected Prime Minister Narendra Modi as a `` historic opportunity '' for the two nations . A firm but simple handshake had sent a message to the world on Monday that the heads of India and Pakistan were ready to talk . And talk they did on Tuesday , in a meeting at Hyderabad House , a former palace in New Delhi , that lasted almost 50 minutes . Briefing reporters after the encounter , Sharif described the meeting as `` good and constructive '' and `` held in warm and cordial atmosphere . '' Sharif said both countries should work to overcome their mutual mistrust , and that regional peace and stability were key to achieving their common goals of development . Sharif said he intended `` pick up the threads '' of the Lahore Declaration , referring to a pledge both countries made in 1999 to cooperate more closely to ease tensions . The Pakistani premier also said that accusations and counter-accusations are not productive -- a comment on the regular political back-and-forth between their two nations . `` We agreed that our meeting should be a historic opportunity for both our countries , '' he said . He added that he was `` very pleased '' to be in New Delhi at Modi 's invitation , having flown in for his counterpart 's inauguration on Monday . Sharif was part of the biggest gathering of South Asian leaders ever assembled for an Indian prime minister 's swearing-in . Emotional response . In a series of tweets posted after Monday 's inauguration ceremony , Modi revealed the two had exchanged remarks . Sharif `` shared some very emotional things , '' Modi said , before recounting a rather strange story Sharif told him about how his mother became emotional while watching television images of Modi 's own mother offering him sweets . In an interview with Indian television station NDTV , Sharif was reported to have described his attendance at Modi 's inauguration as a `` great opportunity , a great moment . '' `` He said that this strong mandate frees up leaders on both sides ... to actually turn a new page in the history of India and Pakistan , '' NDTV 's Barkha Dutt said . Long dispute . Relations have been strained between the two countries since 1947 , the year the Asian subcontinent partitioned into Islamic Pakistan and Hindu-majority India as it gained independence from British rule . In the decades since , they have fought a number of wars and clashed over Kashmir , an 86,000 square-mile region to the north . Efforts to agree a peace deal took a major step back in 2008 when Pakistani militants attacked the Indian city of Mumbai , killing more than 160 people in a series of co-ordinated assaults . In 2011 , the two countries agreed to return to the negotiating table and since then relations have continued to thaw . In 2012 , former President Asif Ali Zardari became the first Pakistani leader to visit India in seven years . He held talks with then Indian Prime Minister Manmohan Singh , who emerged from the 30-minute meeting saying both nations were willing to find `` practical and pragmatic '' solutions to their differences . Zardari described the talks as `` fruitful . '' Sharif is said to have expressed the same optimism for the countries ' relationship in his interview with NDTV on Monday . `` Both governments have a strong mandate . This could help in turning a new page in our relations , '' Sharif told NDTV . `` We should remove fears , mistrust and misgivings about each other . Both countries should rid the region of instability and security that has plagued us for decades . '' Modi 's meeting with Sharif is one of a series of bilateral meetings scheduled with regional leaders on his first day as India 's 15th prime minister .
NEW : Pakistan 's Nawaz Sharif says meeting with India 's PM Modi was warm , constructive . NEW : The two prime ministers will try to overcome mistrust and work together , says Sharif . NEW : India : ` ` We think our meeting should be a historic opportunity for both our countries '' The leaders shook hands on Monday at Modi 's office .