(Adds details, quotes)
* Kremlin: Statehood not goal, region should stay in Ukraine
* Putin says cannot stand by on Ukraine conflict
* But does not acknowledge direct Russian involvement
Aug 31 (Reuters) - President Vladimir Putin called on Sunday for meaningful talks between pro-Russian rebels in eastern Ukraine and the Kiev government on issues including "political organisation and statehood" to protect people living there.
Asked about Putin's remarks quoted by Tass news agency, a Kremlin spokesman said the president was not calling for a separate state in the region, adding it should remain part of Ukraine and calling the crisis there a domestic conflict.
"Substantive, meaningful talks should begin immediately ... related to the issues of society's political organisation and statehood in southeastern Ukraine to protect legitimate interests of people living there," Tass quoted Putin as saying.
Asked later about Putin's remarks, his spokesman Dmitry Peskov told reporters in the Russian city of Chelyabinsk: "This is not a conflict between Russia and Ukraine, this is a domestic Ukrainian conflict."
Pressed on whether Moscow felt that "Novorossiya" - the name the rebels give to the widely Russian-speaking region in dispute - should remain part of Ukraine, Peskov said: "Of course."
"Only Ukraine can reach an agreement with Novorossiya, taking into account the interests of Novorossiya, and this is the only way to reach political settlement," Peskov said.
Kiev and its allies in Europe and the United States - who have imposed sanctions against Russia over its role in Ukraine - say a new separatist offensive in its east has been backed by armoured columns of more than 1,000 Russian troops.
Putin told Russia's state TV Channel 1: "It must be borne in mind that Russia cannot stand aside when people are being shot at almost at point blank," but he did not acknowledge direct Russian intervention in the conflict.
He has repeatedly denied Russian troops are involved and accused Kiev of using excessive force against Russian speakers.
Asked if it was possible to predict the end of the crisis in Ukraine, RIA news agency quoted Putin as telling the TV channel: "No. It largely depends on the political will of current Ukrainian authorities."
Putin added that his meeting with Ukrainian President Petro Poroshenko in Minsk last week was "good", calling Poroshenko a "partner with whom it is possible to have a dialogue".
On Saturday, Poroshenko said he was hoping for a political solution, but warned that Ukraine - like Russia a former Soviet republic - was on the brink of full-scale war. (Reporting by Katya Golubkova and Vladimir Soldatkin; Editing by Richard Balmforth and Mark Heinrich)