He will hold official talks with his Bangladesh counterpart Sheikh Hasina at the Prime Minister's Office.
South Korean Prime Minister Lee Nak-yon paid tributes to the memories of Liberation War martyrs by placing wreaths at the National Mausoleum on Sunday morning.
He later signed the visitors' book and planted a sapling.
The Korean Prime Minister is scheduled to visit Youngone Hi-tech Sportswear in Savar EPZ and the National Institute of Advanced Nursing Education and Research at Mugdapara in the city.
Lee arrived in Dhaka on Saturday on a three-day official visit seeking greater engagements between the two countries to further strengthen the bilateral relations.
He will hold official talks with his Bangladesh counterpart Sheikh Hasina at the Prime Minister's Office (PMO) on Sunday afternoon.
They are likely to discuss ways of cooperation in the areas of security, trade and investment, people-to-people and cultural exchanges.
The prime ministers will witness the signing of bilateral documents after the talks. Prior to that, they will have a tête-à-tête.
A number of bilateral instruments on trade, investment and cultural fronts are likely to be signed.
Bangladesh will seek Korean investment and innovative solutions to help produce diversified products meeting global requirements, officials said.
A Memorandum of Understanding (MoU) between Bangladesh Investment Development Authority and Korea Trade-Investment Promotion Agency (KOTRA) and a document on cultural exchange programme between Bangladesh and South Korea for the years 2019-2023 are likely to be signed, an official told UNB.
Another MoU on cooperation between the Korea National Diplomatic Academy and Bangladesh's Foreign Service Academy is also on the table to sign, said the official.
The South Korean Prime Minister will meet President Abdul Hamid on Sunday evening at Bangabhaban.
He will deliver the keynote speech at Bangladesh-Korea Business Forum to be jointly organised by the Federation of Bangladesh Chambers of Commerce and Industry (FBCCI) and Korea International Trade Association (KITA) at a city hotel on Sunday.
In the evening, he will join a banquet to be hosted by Prime Minister Sheikh Hasina at Hotel Pan Pacific Sonargaon.
On Monday, he will pay homage to the memories of Father of the Nation Bangabandhu Sheikh Mujibur Rahman by placing wreaths on his portrait at Bangabandhu Memorial Museum at Dhanmondi in the city.
Lee will sign visitors' book there after visiting the museum.
The South Korean Prime Minister is scheduled to leave Dhaka at 11am on Monday by a special flight.
Foreign Minister Dr AK Abdul Momen will see off the Korean Prime Minister at Hazrat Shahjalal International Airport.
The South Korean Prime Minister will visit Tajikistan, Kyrgyzstan and Qatar after visiting Bangladesh as part of his four-nation tour from July 13-21. The visits are aimed at strengthening Seoul's ties with Central Asia and Southwest Asia with a balanced diplomacy in the Middle East.