Modi, who arrived here this morning on his maiden official visit to Nepal, met Koirala at Singha Durbar Secretariat.
The two leaders discussed various facets of longstanding mutual relations and issues of common interest.
Earlier, Modi, the first Indian Prime Minister to pay a bilateral visit to Nepal in 17 years, was given a rousing welcome with his counterpart receiving him at the Tribhuvan International Airport, deviating from protocol for the purpose.
Deputy Prime Ministers Bam Dev Gautam and Prakash Man Singh were also present at the airport.
Nepalese Foreign Minister Mahendra Pandey paid a courtesy call on Modi and briefly discussed some bilateral issues, including hydro-power, trade, energy and security.
The meeting took place at a five star hotel an hour after Modi arrived here on a two-day trip, becoming the first Indian Prime Minister to pay a bilateral visit to Nepal in 17 years.
"The talks were held in a very cordial and friendly atmosphere," Pandey told PTI after the meeting.
Modi, in his pre-departure statement summing up the sentiment attached to the two-day trip, had said, "I am excited about my visit and pleased that I am able to go there within weeks of assuming office as Prime Minister."
Modi had said that he looks forward to working with the Nepalese leadership to forge a "new relationship" by identifying steps to strengthen bilateral cooperation in key sectors, including trade and investment, hydropower, agriculture and agro-processing, environment, tourism, education, culture and sports.