WASHINGTON (Reuters) - The United States said on Thursday that Russia was firing artillery across its border with Ukraine to target Ukrainian military positions in the conflict with pro-Russian separatists.

State Department spokeswoman Marie Harf also said there was evidence that the Russians intended to deliver heavier and more powerful multiple rocket launchers to the separatist forces.

Harf, speaking at a regular media briefing, cited intelligence reports but said she could give no more information of what the reports were based on.

A U.S. official, who spoke on condition of anonymity, said the artillery fire began on or after this Tuesday. The official declined to say what targets had been hit but said the United States had no evidence of civilian casualties.

The United States learned about the artillery fire through "technical and overhead" intelligence systems, the official said, an apparent reference to spy satellites and signals-intelligence collection.

Russia has in the past denied it is directly involved with the rebellion in its western neighbor, but the United States and its European allies accuse Moscow of arming and encouraging the uprising and have imposed sanctions on Moscow in response.

A senior U.S. official said during the last week, the United States had become aware of activity involving multiple rocket launch systems at a military base near the town of Rostov, in southwest Russia. U.S. officials say they believe Ukrainian separatists had gone there to train on the weapons.

The U.S. officials said such rocket systems have continued to "depart and return to Rostov at irregular intervals."

Ukraine's Security Council said on Wednesday preliminary information indicated that missiles that brought down two government fighter jets over eastern Ukraine were fired from Russia.

Russia's Defense Ministry on Thursday dismissed this, saying it was "an attempt to mislead the public," Interfax news agency reported, citing a defense ministry official.

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The United States has said it believes a Russian-made SA-11 ground-to-air missile fired from rebel-held territory in eastern Ukraine brought down a Malaysian Airlines jetliner last Thursday, killing the nearly 300 people on board.

One U.S. official said that American agencies knew Ukrainian separatists were in possession of SA-11 missiles before the crash but that their understanding was that they were "defunct" and inoperable.

Earlier this week, U.S. intelligence officials said that the United States only realized that the separatists had operational SA-11s after the Malaysian airliner was shot down.

(Reporting by David Storey, Mark Hosenball and Phil Stewart; Editing by Eric Beech and Steve Orlofsky)