A spokesman for Mr Kiriyenko told reporters near Nazran, the capital of neighbouring Ingushetia, that the prime minister would brief the media after discussions on the future of the region and its demands for aid from Moscow.
Mr Kiriyenko, who was instructed to arrange the meeting by President Boris Yeltsin last week, arrived at the out-of-town residence of the Ingush president, Ruslan Aushev, in an armoured motorcade. Mr Maskhadov apparently was waiting there.
Mr Kiriyenko said after flying in to Vladikavkaz, capital of another region in the ethnic patchwork of the north Caucasus, that he expected a "normal, constructive conversation" with Mr Maskhadov, who signed a peace treaty last year after leading victorious rebel forces.
Mr Kiriyenko admitted last week that Moscow had failed to fulfil its obligations to the rebel region under a peace treaty signed by Mr Yeltsin and Mr Maskhadov over a year ago.
Mr Maskhadov says Moscow has withheld reconstruction funds in a tactic to keep Chechnya unstable after Russian troops pulled out in August 1996 following their bloody but unsuccessful 21-month war against the guerrillas.
Mr Maskhadov, who is seen in Moscow as a relative moderate, survived a car bomb attack 10 days ago. His forces clashed with radical Islamic paramilitaries on 15 July.
He said he was still striving for good relations with Moscow and for a common economic and defence space, but added that he was tired of unfulfilled promises and believed some forces in Moscow were trying to provoke civil war among the million or so Moslem Chechens.
He said he would be asking Mr Kiriyenko when Russia, which is facing a financial crisis of its own, would make good promises to help rebuild the Chechen economy. - ReutersReuse content