By Olivia Siong
Mr Widodo is on his first official visit to Singapore, since taking office in October last year.
Addressing the media after a meeting, Mr Lee said both sides discussed how to increase economic cooperation between Singapore and Indonesia.
He noted that Singapore has consistently been a top trading partner and investor in Indonesia. Indonesia has also always been an attractive destination for Singapore companies.
"We agreed to work together to make it even more attractive, so that Singapore companies can take advantage of opportunities in Indonesia," said Mr Lee.
One example is in the Batam, Bintan and Karimun Special Economic Zone. Mr Widodo added that Indonesia will set up a special unit to handle issues there.
Both sides also spoke about tourism cooperation.
Mr Lee said as Indonesia develops more tourism destinations and resorts, Singapore can promote together with Indonesia as joint destinations. Mr Widodo adding that Singapore and Indonesia can be packaged as a tourist destination.
Both parties also discussed security cooperation and exchanging intelligence between its security agencies.
Mr Lee said Singapore and Indonesia share are concerned with the threat of extremism and the ISIS militant group. Both countries also have nationals involved in terrorist activities, including in the Middle East.
SINGAPORE, INDONESIA SIGN AGREEMENTS
Mr Widodo and Mr Lee also witnessed three agreements being signed between Singapore and Indonesia.
The first was a Memorandum of Understanding (MOU) on electronic government cooperation to facilitate the sharing of experiences and knowledge on the development of electronic government. The second was an MOU on youth and sports cooperation.
The third agreement was a strategic cooperation agreement between the Indonesia Chamber of Commerce and Industry (KADIN) and the Singapore Business Federation (SBF), which aims to improve economic cooperation between the two business chambers. This is the first such agreement between two apex chambers in ASEAN, according to SBF.
Mr Widodo called on Singapore companies to strengthen business cooperation with their Indonesian counterparts as well. Speaking at the Singapore-Indonesia Business Dialogue, Mr Widodo said even though the region is facing a cyclical downturn, there is opportunity for investment.
The dialogue, organised by IE Singapore, SBF and KADIN, was aimed at allowing business leaders to meet Mr Widodo to discuss partnership opportunities in Indonesia.
"We will continue to grow and strengthen our close ties with Indonesia," Mr Lee wrote in a Facebook post on Tuesday evening.