Mongolian border guards check vehicles arriving from Russia at the Mongolian border checkpoint of Altanbulag, Mongolia, on September 25, 2022, after the Kremlin announced a partial mobilisation for the war in Ukraine. AFP
"Recently we've had many people from Russia coming here," Kassym-Jomart Tokayev was quoted as saying by his press service.
"Most of them are forced to leave because of the hopeless situation. We must take care of them and ensure their safety," he added.
"This is a political and humanitarian issue," he said.
The Kazakh leader also condemned Moscow's invasion of Ukraine and called for respect of territorial integrity, as Russia held annexation referendums in four Ukrainian regions.
"The territorial integrity of states must be unshakeable. This is a key principle," he said.
"In our immediate vicinity a major war is underway. We must remember this, thinking above all about our security," Tokayev added.
President Vladimir Putin last week announced the call-up of thousands of reservists for the conflict in Ukraine, sparking protests across the country and a rush among Russian men for the borders.
According to Kazakhstan's interior ministry, around 98,000 Russians entered the country since the mobilisation was announced on September 21, while just over 64,000 left, the RIA Novosti news agency reported.
Meanwhile, long queues to leave the country formed at Russia's border with the Caucasus nation of Georgia, with officials admitting an "extremely tense" situation at the border checkpoint, the regional interior ministry said.
The ministry added that a mobile mobilisation office will be set up at the border checkpoint in the "near future".