Russia and the United States have finished the main part of talks on a new arms-control treaty but have set no date to sign, representatives of both powers said Thursday.

"The delegations are through with the main part of the negotiations," Russian Foreign Ministry spokesman Andrei Nesterenko said.

"We are on the brink of finalizing" a new START arms-control agreement, another Russian official told CNN. "There are some little issues, some trifles," said the official, who has knowledge of the negotiations but was not authorized to speak on the record.

Negotiators, he said, are "almost there."

Similar comments came from Washington, where State Department spokesman Mike Toner said Wednesday that talks for a successor to the Strategic Arms Reduction Treaty were "almost at the finish line." A deal is "really close," he said.

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– CNN's Maxim Tkachenko in Moscow and Jill Dougherty and Charley Keyes in Washington contributed to this report.