After initially trying to distance itself from Russia following Moscow's full-scale invasion of Ukraine, the central Asian country seems to be warming to a "gas union" idea that Putin proposed last year and which would also involve Uzbekistan.
"We are interested in making full use of our transit potential and are ready to further increase the volume of Russian gas transportation," Tokayev was quoted as saying.
Keen to boost sales of its energy and commodities in Asia, after being hit by Western sanctions over its invasion of Ukraine, Putin proposed the "gas union" idea late last year to support shipments between the three countries and to other energy buyers, including China.
Moscow calls its actions in Ukraine a "special military operation."
Last month, Russia started supplying natural gas to Uzbekistan via Kazakhstan, marking the occasion with ceremonies in Moscow and elsewhere attended by the presidents of the three countries and shown on state TV.
The project, Tokayev told Izvestia, "will give a powerful impetus to the industrial development of our countries".
While Russia is a major natural gas exporter, Uzbekistan and Kazakhstan produce roughly as much as they consume. Their outputs, however, are becoming increasingly insufficient as consumption rises, spurred by population growth and industrial development.
A huge increase in liquefied petroleum gas prices early last year led to unrest in Kazakhstan's cities while a shortage of natural gas and electricity amid frigid temperatures sparked protests in Uzbekistan at the start of this year.
The two countries are connected by a gas pipeline to Russia, and a separate pipeline crosses both on its way to China.
However, both pipelines mostly pump gas from Turkmenistan, while Kazakhstan and Uzbekistan have never reported any transit shipments of Russian gas to China or any other countries.
Tokayev also said that Kazakhstan was ready for greater cooperation with Russia in the oil sector - including in transporting Russian oil. He said that plans called for a shipment of up to 100 million metric tons of Russian oil to China by 2033.
Putin, interviewed by the Kazakhstanskaya Pravda daily before his trip, indicated that energy issues will be a big part of his talks with Tokayev.
"Nature and geography give Russia and Kazakhstan significant competitive advantages in the energy sector, which we strive to make the most of for the benefit of our fellow citizens," Putin said.
