Speaking to journalists after their meeting, Kučinskis said they had enjoyed a "very constructive conversation" on various European Union and security questions.
On the EU, Latvia and Denmark have "very similar" views on supporting "pragmatic reforms" Kučinskis said, and praised Denmark as one of Latvia's most supportive partners.
The Latvian PM also urged enhanced cooperation in the area of "biomedicines" and digitalization between the Baltic and Nordic states.
"The Nordic and Baltic region has the potential to become a leader in digitization. Latvia is among the signatories of the Digital North Declaration and is interested in working as closely as possible on the development of a digital single market in the Nordic and Baltic region, " said Kučinskis.
He also praised Denmark's commitment to Latvia's security by sending troops to bolster NATO's enhanced Forward PResence (eFP) mission (Danish troops are stationed in Estonia) and Danish rotations of the Baltic Air Police mission, a role four Danish F-16 jets are currently fulfilling from a base in northern Lithuania also visited by Lokke Rasmussen earlier in the day. He certainly took his inspection seriously as this video he posted shows.
"These practical measures prove that cooperation between the two nations is real and not just on the level of formal phrases of good intent," said Kučinskis.
Rasmussen said he was pleased to announce the Danish crown prince couple would be visiting Latvia later in the year to help celebrate the centenary.
On defense, he said: "We have a shared interest in ensuring the security of our common neighborhood. Russia's behaviour has created an unstable and unpredictable security environment in the Baltic Sea region, which is our neighborhood."
"Denmarks contribution to NATO's enhanced Forward Presence is a clear testimony to our allies and to Russia of NATO's cohesion, solidarity and consequently our commitment to Article 5," Rasmussen added, referring to the obligation of NATO member states to treat an attack on one as an attack on all.
"Denmark remains firmly behind our Baltic friends," he stated.