* On campaign trail, Putin says no "chill" in U.S. ties
* But Syria shows Russia will not play 'yes man' to the West
* Warns U.S. not to ignore Russia's growing military (New throughout)
By Darya Korsunskaya
SAROV, Russia, Feb 24 (Reuters) - Vladimir Putin said on Friday he sees no new chill in ties with Washington, but warned that Russia would not let the United States gain nuclear supremacy and had no intention of playing "yes man" to the West on global issues.
Nine days before a vote almost certain to hand him a six-year presidential term, Putin was chiseling his image as a tough leader of a resurgent Russia prepared to stand up to the United States when necessary.
After a campaign in which he has rounded on Washington, accusing it of encouraging the biggest opposition protests of his 12-year rule, Putin suggested his rhetoric did not mean there was any kind of new Cold War.
"I don't think there is some kind of chill," he said in a meeting with security analysts near a research centre for Soviet and Russian nuclear weapons programmes.
But Russia's veto of a U.N. resolution condemning President Bashar al-Assad's crackdown of dissent in Syria showed it could take a firm stance against the West when it wanted, he said.
"I think our position on the Syrian issue in the U.N. Security Council shows that we do not intend to play along with anyone," Putin said when an analyst suggested it was time "for Russia to stop playing along with the Americans on everything."
As Western and Arab states met in Tunisia to discuss Syria, Putin said he opposed Western moves to despose governments they did not like in places like Damascus and Tehran.
"So, they changed regimes in North Africa, and what will they do now? ... It's unclear what kind of regime Egypt will have and what they are wreaking in Syria is unclear," he said.
"They are trying to take the situation under control but how it will end nobody knows, including them."
Putin also vowed he would stand his ground in a dispute over U.S. plans for a European anti-missile shield, which the Kremlin says could upset the balance of power between the two nations with 95 percent of the world's nuclear arms by increasing capability to shoot down Russian missiles.
"They do not want to discuss this with us seriously," Putin said of the United States. "In our view, an attempt is being made to destroy this balance and create a monopoly - for themselves - on invulnerability."
Russia and the United States signed a landmark treaty in 2010 to put new limits on long-range, offensive nuclear weapons such as Intercontinental Ballistic Missiles (ICBMs), but the dispute over missile defence has clouded relations since then and made further reductions in nuclear weapons unlikely.
Russia wants the United States to offer legally binding assurances that its missile shield could not be used to weaken Russia's offensive arsenal, a demand that is a non-starter in Washington.
Putin has pledged 23 trillion roubles ($790 billion) over a decade to modernise Russia's weaponry and said Russia's growing might should give it a stronger voice in negotiations on issues such as missile defence - one Washington should not ignore.
"We do have something that it seems to me should nudge our colleagues and partners toward more constructive work than we have seen so far," Putin said.
The United States, just a few years ago, had been telling its NATO allies: "'Let Russia tinker, we don't really care, all they've got left is some rust.'" Putin said.
"It's not so - today that is not so at all," he said, describing the missiles, submarines and other weapons Russia has put on duty in recent years. "This is no joke."
"So, we very much hope that together with our partners, acknowledging our responsibility before our people and before all mankind, will work cooperatively to hold back a nuclear arms race," he said. "We not allow a nuclear arms race."
At the same time, Putin made clear Russia would not take further disarmament decisions lightly, and would not give up nuclear weapons until it has high-precision conventional weapons that are comparably powerful.
"Not a single day sooner - and nobody should have any illusions about that," he said.
($1 = 29.1350 Russian roubles) (Reporting by Darya Korsunskaya; Writing by Steve Gutterman; Editing by Robin Pomeroy)