U.S. Defense Secretary Chuck Hagel speaks during the opening of the "National Reading of the Names" ceremony near the Vietnam Memorial in Washington May 24, 2014. REUTERS/Joshua Roberts

SINGAPORE (Reuters) - Russia has withdrawn most of its troops from the Ukrainian border, but seven battalions, amounting to thousands of men, remain, a U.S. defense official said on Friday.

U.S. Defense Secretary Chuck Hagel, in Singapore to attend a weekend security conference, has called the withdrawal of thousands of Russian troops from the border a promising sign, but said all troops positioned there earlier this year needed to be moved back.

The defense official said that most of the troops had been pulled back.

“The majority have gone,” he told reporters. “But seven battalions remain.” The official said he had no figure for the number of troops that had withdrawn. “But ... thousands still remain,” he said.

Hagel, speaking earlier on the plane taking him on a trip to Asia and Europe, said it was known that “thousands of Russian troops have been pulled back and are moving away. We also know that there are still thousands of Russian troops still there that have not yet moved.

“Any time you are moving troops away and equipment and assets away, that’s promising, but they are not where they need to be and won’t be until all of their troops that they positioned along that border a couple of months ago are gone.

The U.S,-led NATO military alliance has previously estimated that Russia had around 40,000 soldiers close to the border.Ukraine’s acting defense minister said on Friday that Ukrainian forces would press ahead with a military offensive against rebels in the east until peace and order had been restored there.

Speaking after 14 servicemen, including a general, were killed on Thursday when rebels shot down an army helicopter, the minister, Mykhailo Koval, said: “Our given task is to bring peace and order to the region.”