* Putin wants "systemic adjustments" to EU-Ukraine trade deal
* Trade conflict is a tug-of-war for influence in Ukraine (Updates with background, Putin's letter to Barroso)
BRUSSELS, Oct 1 (Reuters) - Amendments to a EU-Ukraine trade deal at the centre of tensions between Russia and the West can only be agreed between Brussels and Kiev, the head of the European Commission has said.
Russian President Vladimir Putin wants to see three-way negotiations to amend the accord, which Russia says will hurt its economy, and has threatened to curtail Ukraine's access to Russian markets if Kiev implements the deal as it is.
"We have strong concerns about the recent adoption of a decree by the Russian government proposing new trade barriers between Russia and Ukraine," Jose Manuel Barroso said in a letter to Putin released by the EU leader's office on Wednesday.
"The Association Agreement (between the EU and Ukraine)remains a bilateral agreement and ... in line with international law, any adaptations to it can only be made at the request of one of the parties and with the agreement of the other," he wrote in response to a letter from Putin to him and Ukraine's President Petro Poroshenko on Sept. 17.
According to EU officials, Russia wants to remove more than 2,000 products eligible for duty-free access to the European Union, accounting for about a quarter of the agreement, in what Putin described in his letter as "systemic adjustments".
The EU-Ukraine trade deal is at the heart of a tug-of-war between the West and Russia that sparked protests in Kiev, brought down the previous government of Viktor Yanukovich and eventually led to the annexation of Crimea by Russia, armed conflict in eastern Ukraine and Western sanctions.
Implementation of the accord, which was signed in June and ratified in September, has been delayed until Dec. 31, 2015, in a concession to Moscow.
Brussels hopes that the 15-month delay will give it time to assuage Russian concerns about the pact, which is now a legal treaty that cannot easily be changed. But Putin's letter, seen by Reuters, suggests the Kremlin considers the delay a complete freezing of the process until its demands for changes are met.
Putin will have his first opportunity to discuss the issue at a summit on Oct. 16-17 in Milan, diplomats say.
The woman set to become the EU's new trade chief later this year, Sweden's Cecilia Malmstrom, told the European Parliament this week that she would not allow Moscow to change the trade pact's text. (Reporting by Robin Emmott; Editing by Sonya Hepinstall)