* Russian rouble recovers after U.S. security response

* Rouble had hit 80.4125 vs dollar, a near 15-mth low

* Currency touches weakest vs euro since late April

* Russian stocks cling to gains as oil prices surge

MOSCOW, Jan 26 (Reuters) - The Russian rouble recovered some ground after the United States delivered written replies on Wednesday to sweeping Russian security demands, having earlier plunged to a near 15-month low versus the dollar as tensions over Ukraine escalated.

In a key step in a fragile diplomatic process as Russia staged new military drills on land and sea near Ukraine, the United States set out a serious diplomatic path forward in the written replies, Secretary of State Antony Blinken said.

Volatility has plagued Russian markets in recent weeks amid Western fears Russia is poised to invade its neighbour, something Moscow has repeatedly denied. The West has threatened sanctions https://www.reuters.com/markets/europe/how-financial-western-sanctions-might-target-russia-2022-01-19 with profound economic effects if Russia does make an incursion.

By 1834 GMT, the rouble was 0.9% weaker against the dollar at 79.30, earlier sliding more than 2% to hit 80.4125, its weakest point since Nov. 2, 2020.

The rouble lost 0.9% to trade at 89.50 to the euro , earlier touching 90.7250 for the first time since late April 2021.

"Geopolitical swings still remain a bet on a binary outcome – the tanks roll across the Ukrainian border or they do not; if they do not, there will be swift upside, if they do, there will be dramatic downside," BCS Global Markets said.

In Paris, four-nation talks dragged on longer than expected on ending a separatist conflict in eastern Ukraine, part of a wider crisis between Moscow and Kyiv that has raised the risk of a full-scale war.

Those talks, involving Russia, Ukraine, France and Germany, could lead to some easing of geopolitical tensions, which would support the rouble, said Sberbank CIB in a note.

Citing persistent volatility, the finance ministry cancelled weekly OFZ treasury bond auctions, usually held on Wednesdays. Russia's 10-year OFZ yields hit their highest since early 2016 at 9.86% early on Wednesday. Yields move inversely to price.

Brent crude oil, a global benchmark for Russia's main export, was up 2.2% at $90.10 a barrel, hitting a more than seven-year high.

Russian stock indexes clung to that support, still attempting to recover from a massive sell-off on Monday.

The dollar-denominated RTS index was up around 2%, while the rouble-based MOEX Russian index gained around 3%.

"Shares in Russian companies are now trading at very low valuations and offer some of the most attractive dividend yields in the world," Alfa Bank said in a note.

(Reporting by Alexander Marrow; Editing by Andrew Heavens and Nick Macfie and Kirsten Donovan)