* Protests over Navalny arrest battering rouble
* Putin calls protests illegal and dangerous
* Rouble hits 75.5825 vs dollar, weakest since Dec. 23
* Touches 91.8000 vs euro, lowest mark since Jan. 5 (Updates prices, adds bullets, Putin & ITI Capital comments)
By Alexander Marrow
MOSCOW, Jan 25 (Reuters) - The Russian rouble gave up early gains to hit more than a one-month low on Monday in volatile trade, hampered by geopolitical risks related to the arrest of Kremlin critic Alexei Navalny and subsequent protests calling for his release.
Police detained more than 3,000 people and used force to break up rallies across Russia on Saturday as tens of thousands of protesters ignored police warnings and extreme cold weather, leading the European Union to consider fresh sanctions against Moscow.
"Any destabilisation of the political situation in the country is always a strong negative both for equities and for the rouble," said Alor Broker analyst Alexei Antonov.
By 1347 GMT the rouble was 0.3% weaker against the dollar at 75.54, having touched its weakest level since Dec. 23 of 75.5825.
It had lost 0.1% versus the euro to trade at 91.73 , earlier hitting its lowest mark since Jan. 5 of 91.8000.
President Vladimir Putin on Monday called the protests illegal and dangerous, as a Navalny ally said more protests would be held on Jan. 31.
The Navalny effect would be felt mostly in terms of foreign policy, like sanctions, said ITI Capital analyst Iskander Lutsko.
"The sanctions themselves will be more pinpointed, not countrywide, and could affect Nord Stream 2," he said.
A pipe-laying vessel has started working in Danish waters ahead of resumed construction of the gas pipeline, amid pressure from the United States and EU to halt it.
The Kremlin on Sunday indicated a willingness to talk with new U.S. President Joe Biden and his administration but, with relations between the two countries languishing at Cold War lows, it also accused Washington of meddling in Saturday's protests.
"Biden's policy towards Russia remains unclear and, given recent news flow, investors may be leery of Russian assets going into this week," BCS Global Markets said.
Brent crude oil, a global benchmark for Russia's main export, was down 0.2% at $55.29 a barrel.
Russian stock indexes were mixed.
The dollar-denominated RTS index was down 0.1% to 1,417.2 points. The rouble-based MOEX Russian index was 0.4% up at 3,397.1 points.
For Russian equities guide see
For Russian treasury bonds see (Additional reporting by Elena Fabrichnaya Editing by Toby Chopra, David Goodman and Paul Simao)