As many as 100,000 Russian troops have been sent to Ukraine’s border supposedly to conduct military exercises – but Pentagon officials say there hasn’t been any proof of that and worry that a full invasion is near.

Pentagon spokesman Rear Adm. John Kirby told reporters on Thursday that the Russians continue to build up along the southern and eastern border with Ukraine. In a phone call last week, Russian Defense Minister Sergei Shoygu assured Defense Secretary Chuck Hagel that the buildup was to conduct “springtime exercises” and assured him that troops would not cross the border.

“We’ve seen no specific indications that exercises are taking place,” Kirby said. “Defense Minister Shoygu assured him that this was for exercise purposes only and that they had no intention of crossing the border. They need to keep their word on that.”

Some estimates have put the number of Russian troops on the border at 100,000. Kirby said he would not “get into estimating specific numbers,” but said they were in the thousands. Earlier, he had said there were as many as 20,000 Russian troops. Officials in Ukraine say the number is closer to 100,000.

“We continue to see the Russian military reinforce units on their side of the border with Ukraine.

We remain concerned about that. We’re monitoring it closely,” he said. The buildup comes after pro-Russian forces annexed Crimea, in southern Ukraine, earlier this month. The United Nations General Assembly called the Russian invasion illegal, rejected Crimea’s referendum vote, and backed a Ukraine that includes Crimea, in a nonbinding resolution passed by vote of 100 to 11, with 58 abstentions.

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“Just because we haven’t seen an indication of exercises now, doesn’t mean that one won’t occur,” Kirby said. “They certainly have amassed troops along that border, they have them in quite a number and in a composition that provides lots of capability.” British Defense Secretary Philip Hammond said in Washington on Wednesday that the Russian military may be following its own “classic” doctrine of building up a large troop presence before beginning their planned de-escalation.

“Even if this is exercises,” Kirby said, “it’s doing nothing to help de-escalate the tension in Ukraine.”

President Barack Obama has said he’s hopeful that Russia will not invade Ukraine and said there is no military solution to the crisis. "With respect to the Russian troops that are along the border of Ukraine at the moment, right now they are on Russian soil. And if they stay on Russian soil, we oppose what appears to be an effort of intimidation, but Russia has a right, legally, to have its troops on its own soil. I don't think it's a done deal. And I think that Russia's still making a series of calculations," Obama said at the Hague on Tuesday.

Meanwhile, Congress passed bills offering aid to Ukraine that were expected to quickly be delivered to the president. Rep. Mike Turner, R-Ohio, chairman of the U.S. delegation to the NATO Parliamentary Assembly, said in a statement Thursday that “over the past week, we’ve seen the buildup of up to 80,000 additional Russian troops along with large amounts of armored ground vehicles, battle tanks, artillery systems as well as rotary and fixed wing aircraft. This buildup is significant and clearly indicates that President Putin is creating options to potentially capture much of Eastern Ukraine and move on Kyiv. While Putin may have indicated to President Obama that he has no intentions of advancing further into Ukraine, his actions clearly indicate the opposite.”