Putin was welcomed by an honour guard the night before as he landed in Ulaanbaatar to begin the high-profile trip, seen as a show of defiance against the court, Kyiv, the West and rights groups that have all called for him to be detained.
The Russian leader is wanted by the Hague-based court for the alleged illegal deportation of Ukrainian children since his troops invaded the country in 2022.
Ukraine has reacted to the trip with fury.
On Monday, it accused Mongolia of “sharing responsibility” for Putin’s “war crimes” after authorities did not detain him at the airport.
Kyiv had urged Mongolia to execute the arrest warrant, while the ICC said last week all its members had an “obligation” to detain those sought by the court.
In practice, there is little that can be done if Ulaanbaatar does not comply.
A vibrant democracy situated between authoritarian giants Russia and China, Mongolia enjoys close cultural links to Moscow as well as a critical trading relationship with Beijing.
It was under Moscow’s sway during the Soviet era.
And since the Soviet collapse in 1991, it has sought to keep friendly relations with both the Kremlin and Beijing.
The country has not condemned Russia’s offensive in Ukraine and has abstained during votes on the conflict at the United Nations.
The Kremlin said last week it was not concerned that Putin would be arrested during the visit.
– ‘Get Putin out of here’ –
The capital’s central Genghis Khan Square, also known as Sukhbaatar Square, was decked out Monday with huge Mongolian and Russian flags for Putin’s first visit to the country in five years.
A small protest gathered in the afternoon, with demonstrators holding a sign demanding “Get War Criminal Putin out of here”.
Another protest is planned at midday Tuesday at Ulaanbaatar’s Monument for the Politically Repressed, which honours those who suffered under Mongolia’s decades-long Soviet-backed communist regime.
Mongolia’s government has not commented on the calls to arrest Putin.
But a spokesman for President Ukhnaagiin Khurelsukh took to social media on Sunday to deny reports that the ICC had sent a letter asking it to execute the warrant when he visits.
Russia does not recognise the jurisdiction of the ICC.
And Amnesty International warned Monday that Mongolia’s failure to arrest Putin could further undermine the ICC’s legitimacy, while emboldening the ex-KGB spy, in power for almost a quarter of a century.
“President Putin is a fugitive from justice,” Altantuya Batdorj, executive director of Amnesty International Mongolia, said in a statement.
“Any trip to an ICC member state that does not end in arrest will encourage President Putin’s current course of action and must be seen as part of a strategic effort to undermine the ICC’s work.”