Kazakhstan is struggling to accommodate tens of thousands of Russians who have fled their homeland since Moscow announced a military mobilisation last week, officials say, but the Almaty government has no plans to close its border.

Russian men, some with families, started crossing the world's second-longest land border en masse after Russian President Vladimir Putin ordered the mobilisation of reservists last week amid a stalled military campaign in Ukraine.

Russians do not need a visa or even a passport to enter Kazakhstan, just their Russian identity papers. The Russian language is also widely spoken in the country, which is home to a large ethnic Russian minority.

However, the sudden influx of Russians - the government says almost 100,000 have crossed the border since the mobilisation announcement - has stretched the infrastructure of the vast but sparsely populated nation. Hotels and hostels are full, and rent has skyrocketed.

Kazakh President Kassym-Jomart Tokayev, whose administration has refused to support what Russia calls a "special military operation" in Ukraine, urged patience and tolerance.

"A lot of people from Russia have come here over the last few days," he said in a speech on Tuesday. "Most of them were forced to leave by the desperate situation."

"We must take care of them and ensure their safety. This is a political and humanitarian matter," Tokayev said.

His government will discuss the situation with Moscow, he said.

At the same time, the interior ministry published a proposal to change immigration rules this week that would limit to three months the time Russians can stay in Kazakhstan unless they have a passport.

While some Kazakhs have already called for border closures or restrictions on Russians' entry, others have arranged meeting points for arriving Russians and set up volunteer networks to help them find shelter.

An Almaty resident told Reuters she took in three young men from Russia on Monday who were preparing to spend the night on the street in the downtown area. In the city of Oral, some Russians have spent a night at a local cinema which invited them through social media.

"I am crashing on my friends' couch right now," said a 32-year-old Russian IT professional who has moved to Almaty and asked not to be named.

"I do not have a clear plan on what to do next, but I am definitely not going back to Russia. I hope to find work here." (Reporting by Mariya Gordeyeva and Olzhas Auyezov; Editing by Angus MacSwan)