(CNN) -- Don't mess with Russia.
That was President Vladimir Putin's message on Friday, the same day a British government source claimed that Russian troops had significantly ratcheted up their military incursion into Ukraine.
Moscow doesn't want or intend to wade into any "large-scale conflicts," Putin insisted at a youth forum, state-run ITAR-Tass reported. A few breaths later, he made the point that Russia is "strengthening our nuclear deterrence forces and our armed forces," making them more efficient and modernized.
"I want to remind you that Russia is one of the most powerful nuclear nations," the President said. "This is a reality, not just words."
He later warned, "We must always be ready to repel any aggression against Russia and (potential enemies) should be aware ... it is better not to come against Russia as regards a possible armed conflict."
The comments came the same day that Foreign Minister Sergey Lavrov accused NATO of using "images from computer games" to -- in his view -- falsely make the case that Russian troops are in Ukraine. Lavrov said "hiding the evidence is an outstanding characteristic of the U.S. and many EU countries" with regard to Ukraine.
The thing is, many in the West don't believe much of anything coming out of Russia.
White House spokesman Josh Earnest said Friday that -- whatever the Kremlin says -- the reality is Russian troops are inside the Ukraine and have fired on Ukrainian military positions.
"Those denials are completely without credibility," Earnest said.
And Russia's military may be digging in deeper in Ukraine. The British government source told CNN on Friday that Russia has moved 4,000 to 5,000 military personnel -- a figure far higher than one U.S. official's earlier claim of 1,000 troops.
The soldiers are aligned in "formed units" and fighting around Luhansk and Donetsk, said the UK source. And they may soon have company: Some 20,000 troops are on border and "more may be on the way," the source adds.
So what's Russia's endgame? Does it simply want to protect civilians or ethnic Russians in Ukraine? Or does it endeavor to develop a land bridge between Crimea -- which split from Ukraine to become part of Russia months ago, amid the unrest following President Viktor Yanukovych's ouster -- and the Russian border? Or perhaps take over all of Ukraine now?
The UK source, giving his government's analysis of Russian troop movements, surmised that right now "the primary role of the current Russian deployments inside Ukraine is probably to assist, support and take the pressure off the separatist forces in order to maintain pressure on Kiev to decentralize.
"However, we are not ruling out more ambitious plans, including a land corridor from the Russian border to Crimea."
NATO chief blasts Russia's 'hollow denials'
Ukraine has been in crisis since last fall, when political upheaval preceded widespread violence that threatened to tear the Eastern Europe nation apart.
If anything, that violence has worsened the past several months -- as pro-Russian rebels dug in and Ukraine's military stepped up its offensive to retake its territory. The U.N. human rights office reports at least 2,593 people killed between mid-April and August 27, and that many innocent civilians have been killed, hurt or trapped in urban areas.
Predictably, both sides have taken the high road while blaming each other for humanitarian crisis and for perpetrating violence rather than having fair, sincere negotiations toward a cease-fire.
"When Kiev said that negotiations would begin only after the surrender of those whom they call 'separatists,' the militia are left with no choice but to defend their homes, their families," Russia's foreign ministry said in a statement.
Western officials say that Moscow hasn't taken any responsibility, whether for its military's on-the-ground involvement or how it can influence rebels.
Speaking after a meeting of NATO ambassadors in Brussels, Belgium, Secretary-General Anders Fogh Rasmussen said what he called "the serious escalation of Russia's military aggression against Ukraine" violates Ukraine's territorial integrity and "defies all diplomatic efforts for a peaceful solution."
"Despite Moscow's hollow denials, it is now clear that Russian troops and equipment have illegally crossed the border into eastern and southeastern Ukraine," Rasmussen said. "This is not an isolated action but part of a dangerous pattern over many months to destabilize Ukraine as a sovereign nation."
Fighting raging on multiple fronts
Whoever is to blame, whoever is involved, two things that are not in question is that the fighting is continuing and that there's no end in sight.
Ukrainian troops have been fighting on two fronts: southeast of rebel-held Donetsk, and along the nation's southern coast in the town of Novoazovsk, about 12 miles (20 kilometers) from the Russian border.
Mykhailo Lysenko, deputy commander of the Ukrainian Donbas battalion, on Thursday described the fighting in the south as "a full-scale invasion."
Analysts suggest that Russia may have sent its forces into Novoazovsk to secure a land route from the border to the Crimean peninsula it annexed from Ukraine in March, and in order to throw Ukrainian forces making gains against besieged rebel forces in the cities of Donetsk and Luhansk off balance.
In a statement issued by the Kremlin, Putin said the rebels had halted a Ukrainian military operation in eastern Ukraine that he said had endangered the civilian population and caused many casualties.
The UK government source said Russian forces are fighting alongside rebels around Luhansk and Donetsk. It's too early to gauge their impact, though even if propping up the pro-Russian separatists for months longer so that Ukraine's military doesn't next turn its attention to taking back Crimea could be considered a victory.
"At the very least, the Russian deployments are creating the conditions for a frozen conflict going into winter and ... ensure that Kiev is sufficiently distracted ... to prevent it from refocusing its attention on Crimea," the source said.
Retired Lt. Gen. Mark Mark Hertling, a 37-year veteran who once commanded U.S. soldiers in Europe, thinks that Russia may be aiming higher than that. If Ukraine folds easily to Russia's military might, neighboring nations might have good reason to worry. On the other side, Moscow could lose sway if its efforts fail.
"He is trying to influence the Europeans, and it won't stop just with Ukraine," the military analyst told CNN, predicting more Russian military intervention elsewhere. "This is something where he is trying to counter the influence of the West, and he can't afford to lose in Ukraine."
CNN's Max Foster, Alla Eshchenko, Elaine Ly and Barbara Starr as well as journalist Victoria Butenko contributed to this report.