* Lavrov, Kerry talk by phone, following Obama and Putin
* West worried by Russian troop buildup near Ukraine
* NATO chief says Crimea "may not be enough" for Putin (Adds details, quotes, background)
By Katya Golubkova
MOSCOW, March 29 (Reuters) - Russia said on Saturday it had "no intention" of invading eastern Ukraine, responding to Western warnings over a military buildup on the border following Moscow's annexation of the Crimean peninsula.
Foreign Minister Sergei Lavrov, speaking on Russian television, reinforced a message from President Vladimir Putin that Russia would settle - at least for now - for control over Crimea despite massing thousands of troops near Ukraine's eastern border. "We have absolutely no intention of - or interest in - crossing Ukraine's borders," Lavrov said.
But he added that Russia was ready to protect the rights of Russian speakers, referring to what Moscow sees as threats to the lives of compatriots in eastern Ukraine since Moscow-backed Viktor Yanukovich was deposed as president in February.
The West imposed sanctions on Russia, including visa bans for some of Putin's inner circle, after Moscow annexed Crimea this month following a referendum on union of the Russian-majority region with the Russian Federation which the West said was illegal.
The West has threatened tougher sanctions targeting Russia's stuttering economy if Moscow sends more troops to Ukraine. U.S. officials said as many as 40,000 may be massed near the border.
NATO Secretary General Anders Fogh Rasmussen, in an interview with Germany's Focus magazine, said the alliance was "extremely worried".
"We view it as a concrete threat to Ukraine and see the potential for further interventions," said Rasmussen, who is due to leave the post in October.
"I fear that it is not yet enough for him (Putin). I am worried that we are not dealing with rational thinking as much as with emotions, the yearning to rebuild Russia's old sphere of influence in its immediate neighbourhood."
In a sign, however, that Putin may be ready to reduce tension in the worst East-West standoff since the Cold War, the Russian leader called U.S. President Barack Obama on Friday to discuss a U.S. diplomatic proposal for Ukraine.
The White House said Obama told Putin that Russia must pull back its troops and not move deeper into the ex-Soviet republic.
The Kremlin said Putin had suggested "examining possible steps the global community can take to help stabilise the situation."
That was followed by a phone call on Saturday between Lavrov and U.S. Secretary of State John Kerry, the Russian Foreign Ministry said. It said they discussed Ukraine and the timing of further contacts on a call initiated by Washington.
Ukraine remains deeply divided over protests that led to Yanukovich's ousting and many eastern Russian-speaking regions are sceptical about the policies of the new pro-Western government in Kiev.
Yanukovich called on Friday for each of the country's regions to hold a referendum on their status within Ukraine, instead of the presidential election planned for May 25.
That election is shaping up as a context between former prime minister Yulia Tymoshenko and billionaire confectionary oligarch Petro Poroshenko, after boxer-turned-politician Vitaly Klitschko withdrew on Saturday.
Lavrov called for "deep constitutional reform" in Ukraine, a sprawling country of 46 million people divided between those who see their future in closer ties with Europe and mainly Russian speakers in the east who look to former Soviet master Russia.
"Frankly speaking, we don't see any other way for the steady development of the Ukrainian state apart from as a federation," Lavrov said.
Each region, he said, would have jurisdiction over its economy, finances, culture, language, education and "external economic and cultural connections with neighbouring countries or regions".
"Given the proportion of native Russians (in Ukraine) we propose this and we are sure there is no other way," Lavrov said, and Russia had briefed Western powers and others on the proposal.
There was also a bid for regional devolution within Crimea. Its Tatar community, an indigenous minority who were persecuted under Soviet rule and largely boycotted last month's referendum on joining Russia, want autonomy on the Black Sea peninsula, the Tatar leader said on Saturday.
(Additional reporting by Alessandra Prentice in Kiev, Gabriela Baczynska in Crimea and Madeline Chambers in Berlin, editing by Matt Robinson and Mark Heinrich)