* EU leaders hail closer cooperation with Russia
* Still 'grave concerns' about human rights in Russia
* Joint modernisation drive launched, but short on details
(Recasts after closing briefings)
By Conor Humphries
ROSTOV-ON-DON, Russia, June 1 (Reuters) - EU leaders hailed warming ties with the Kremlin at a summit on Tuesday, but warned that Moscow was falling short in its bid to achieve the modern, democratic state President Dmitry Medvedev has called for.
At the end of two days of talks filled with friendly words, but marred by a police crackdown on opposition protesters, EU President Herman Van Rompuy said Europe retained grave concerns about human rights in Russia and called for swift reforms.
"The modernisation of Russia has to become reality ... With Russia, we do not need a 'reset'. We want a 'fast forward'," Van Rompuy said, referring to President Barack Obama's attempts to 'reset' U.S. relations with Moscow.
Relations between Moscow and Brussels have improved sharply in recent months after a dramatic reconciliation between Russia and Poland, but the two-day summit in the southern Russian city of Rostov-on-Don exposed the limits to cooperation.
The two sides officially launched a Programme for Modernization under which the EU has promised to provide investment, training and technology in return for reforms to open up Russia's economy and society.
But there was no clear progress on demands that the EU reduce visa barriers to Russians visiting Europe and open strategic European firms to Russian investment.
CIVIL REFORMS
And the EU made clear it was not satisfied with Medvedev's efforts to boost human rights and civil society in Russia.
"The situation for human rights defenders and journalists in Russia is of grave concern to the European public at large," Van Rompuy said at a briefing after his first twice-yearly Russian summit as EU president.
Human rights and democracy have long been a thorn in ties between Russia and the West, although tensions have eased somewhat since Medvedev took over from Vladimir Putin in 2008 with a pledge to boost civil society.
Rights groups including Amnesty International and Human Rights Watch (HRW) urged the EU not to let Medvedev off lightly.
At the start of talks on Tuesday, Van Rompuy suggested Russia must expand democracy in order to modernise.
"Your choice to base Russia's modernisation in the 21st century on democratic values and building a modern economy implies significant development," Van Rompuy said.
But Van Rompuy voiced no criticism of Russia's uncompromising handling of opposition protests that took place in Moscow and St Petersburg during a summit dinner on Monday evening. More than 150 people were detained. [
].On the financial front, Medvedev praised European efforts to solve the EU financial crisis.
He reminded EU leaders that 41 percent of Russia's $450 billion in currency reserves are held in euros, but did not offer any assurances that Russia would not sell some.
MODERNISATION
Medvedev, who has made modernisation and innovation watchwords of his presidency, says European technology is needed to wean the economy, which slumped 7.9 percent last year, off its reliance on energy exports.
For its part, the EU is hoping to boost trade with Russia.
After rising for nearly a decade, EU exports to Russia fell sharply during the financial crisis, dropping to 66 billion euros ($80 billion) last year from 105 billion euros in 2008.
The summit declaration announced the official launch of the Programme for Modernisation. But it gave no deadlines, saying that the sides were "committed to working together to address common challenges with a balanced and result-oriented approach".
Before the summit, Russian officials expressed impatience at the lack of progress in securing visa-free travel to Europe for Russians, two decades after the fall of the Iron Curtain.
But the EU refused to set a date for an agreement. "We remain committed to making concrete progress as soon as possible on the ground," Van Rompuy said.
The Kremlin has watched in frustration as, despite the post-Soviet economic recovery, the EU scrapped visa requirements for poorer states such as Bosnia and Albania, but not Russia.
EU officials fear dropping visas could spark a wave of overstayers and a backlash among voters in western Europe. (Writing by Conor Humphries; Editing by Kevin Liffey)