A host of strategic issues, including defence and security, were discussed between Modi and Koirala during their talks that lasted 40 minutes.
Talking about bilateral ties, Modi said, "When we trust each other, we can move forward quickly. Projects that have been in limbo for 25 years are moving forward. I feel very satisfied," he said, inaugurating a trauma centre built by India at Kathmandu's Bir Hospital.
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The agreement for Line of Credit to the neighbouring state was signed between Nepal finance ministry's Joint Secretary Madhu Kumar Marasini and Deputy Managing Director of Exim Bank David Rasquinha.
Modi, who arrived here earlier on Tuesday for a three-day visit, will attend the two-day 18th Saarc (South Asian Association for Regional Cooperation) Summit, beginning on Wednesday, apart from holding bilateral meetings with other Saarc leaders.
India and Nepal signed the Motor Vehicle Agreement under which permit would be given to vehicles to ply on designated routes in each other's country.
They also inked three twin-city pacts between Kathmandu-Varanasi, Janakpur-Ayodhya and Lumbini-Bodh Gaya.
The 10 agreements also include, memoranda of understanding on training at Nepal Police Academy, tourism, traditional medicines and youth exchange.
A pact was also signed on a project development agreement over the 900 megawatt hydro-electric project on the Arun river in Nepal.
"We have decided to allow our nationals to carry Rs 500 and Rs 1,000 denomination notes up to the limit of Rs 25,000," Prime Minister Modi announced.
India also gifted Nepal a mobile soil testing lab to boost soil health monitoring and adoption of best agricultural practices.
Modi made a strong pitch for the early drafting of Nepal's Constitution, saying if the country fails to do so, it may get into "difficulties".
He said India will not like to interfere but having expertise and not being able to help Nepal from getting into difficulty will be sad.
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