White House national security adviser Jake Sullivan warned Sunday that Russia will face "severe economic consequences" from the United States and Western allies if it invades Ukraine.

"In terms of sanctions, what we have laid out is a very clear message to the Russians, and we've done so in concert and in unison with our allies that if they do further invade Ukraine, there will be severe economic consequences and a price to pay," Sullivan said in an interview with "Face the Nation." "If it turns out that Russia is pummeling Ukraine with cyberattacks, and if that continues over the period ahead, we will work with our allies on the appropriate response."

The Biden administration has been pursuing a diplomatic response to the build-up of tanks and more than 100,000 Russian forces along Ukraine's eastern border, and it has been clear it prefers the diplomatic route. U.S. and Russian diplomats met in Geneva, Switzerland, last week to try to defuse the security crisis involving Ukraine.

Still, Sullivan said that if Russia does take military action, the U.S. will "take measures that go at their economy, that go at their strategic position in Europe, that strengthen the solidarity of NATO."

"We're ready either way. If Russia wants to move forward with diplomacy, we are absolutely ready to do that in lockstep with our allies and partners. If Russia wants to go down the path of invasion and escalation, we're ready for that too, with a robust response that will cut off their strategic position," he said. "So, from our perspective, we are pursuing simultaneously deterrence and diplomacy, and we've been clear and steadfast in that again, fully united with the transatlantic community."

The threat of a Russian invasion into Ukraine has continued to intensify, and U.S. officials believe Russian President Vladimir Putin could order military action as soon as this month or February. While Russia has sent mixed signals about a possible invasion, it has not indicated there will be a reduction in its troop presence, and Putin has demanded NATO scale back its troop presence in Eastern Europe, among other security guarantees.

Amid the rising tensions, Ukrainian government servers were hit with a cyberattack late last week that brought government websites down. Hours before the cyber offensive, Ukrainian Ambassador to the U.S. Oksana Markarova told CBS News the country believes such an attack would come before major military action by Putin's troops.

Sullivan said the Biden administration has been warning for months that cyberattacks could be part of a "broad-based Russian effort to escalate in Ukraine," and the U.S. has been working with the Ukrainian government to harden their defenses.

"That's part of their playbook. They've done it in the past in other contexts," he said.

Still, Sullivan said the Biden administration has not yet attributed the cyberattack, but added, "it would not surprise me one bit if it ends up being attributed to Russia."