Russia-Ukraine updates: 2 US veterans who joined Ukrainian forces missing

The United States has seen "limited" Russian offensive operations southwest of Donetsk and south of Izium in eastern Ukraine, a senior U.S. defense official said Tuesday, describing the military activity as "preludes to larger offensive operations that the Russians plan to conduct."

"These are actual ground offensives, and they are being supported, of course, by some long-range fires, mostly artillery, which is right out of the Russian doctrine," the official said.

But while there is ongoing fighting in the region, a more devastating offensive strategy appears to be still in the works, according to the official.

Both Ukrainian President Volodymyr Zelenskyy and Russian Foreign Minister Sergei Lavrov have said Russia's new offensive has started in the Donbas region. But the U.S. defense official said it does not appear the new offensive has begun in earnest.

"We think that these offenses are preludes to larger offensive operations that the Russians plan to conduct," the official said. "So we're not pushing back on the notion that offensive operations have begun, but again, we think that this is a prelude of larger offensive operations that are potentially still in the offing here."

The Pentagon believes Russia's military is assessing the mistakes it made in fighting in the north, where it was plagued with logistical and supply problems. U.S. defense officials suspect Russia is conducting what they describe as "shaping operations" to set favorable conditions on the battlefield before beginning its new offensive in earnest.

"In other words, continue to reinforce, continue to make sure they have logistics and sustainment in place, continue to make sure that they have proper aviation and other enabling capability," the official said.

Over the last 24 hours, two Russian battalion tactical groups comprised of about 2,000 combat troops have been sent into Ukraine, according to the official. It's now estimated that 78 Russian BTGs are inside the country, all in the south and east.

-ABC News' Matt Seyler

Polish Prime Minister Mateusz Morawiecki visited western Ukraine Tuesday to mark the opening of a temporary housing community his country donated for Ukrainians displaced by the war.

“This is short term container housing. Conditions here are typically temporary, just for those people who just have nowhere to go,” Morawiecki said during his visit to Lviv.

Morawiecki said Polish teams would also be going to Bucha and Kyiv Tuesday to build more temporary houses.

“Russia is not only ruining all foundations of people’s life in Ukraine, it burns everything to plain concrete and only smoke and ash remains," Morawiecki said.

The prime minister said nearly 10 million people have been forced to leave their homes in Ukraine since the start of the Russian invasion on Feb. 24 and 2.5 million of the displaced residents have sought refuge in Poland.

"But we have to remember that approximately 6 million are still staying somewhere in Ukraine," Morawiecki said.

-ABC News' Yuri Zalizniak

Canada's Foreign Ministry announced Tuesday new restrictions will be imposed on 14 close associates of the Russian regime, including Russian oligarchs, their family members and the two adult daughters of Russian President Vladimir Putin.

The move come after the United States imposed sanctions April 6 on Putin's daughters, Katerina Vladimirovna Tikhonova and Maria Vladimirovna Vorontsova. A senior Biden administration official said there was reason to believe that Putin and his associates hide their wealth with family members and that was the reason they were being targeted.

Since Russia’s invasion of Ukraine on Feb. 24, Canada has imposed sanctions on more than 750 individuals and entities from Russia, Ukraine and Belarus.

Canada has referred the situation in Ukraine to the International Criminal Court (ICC) in concert with other ICC member states as a result of numerous allegations of serious international crimes alleged against Russian forces in Ukraine, including war crimes and crimes against humanity.

Russian Defense Minister Sergei Shoigu has accused the United States and other Western countries of doing everything in their power to drag out Russia's so-called special military operation in neighboring Ukraine.

"The increasing volume of foreign arms supplies clearly demonstrates their intentions to provoke the Kyiv regime to fight to the last Ukrainian standing," Shoigu told officials during a televised meeting Tuesday.

Shoigu said it is important Russia continue improving its armed forces in light of recent events in Ukraine.

Shoigu added that the Russian army is "fulling the tasks set by the commander-in-chief." He said a new offensive in eastern Ukraine's disputed Donbas region is "being consistently implemented, and measure are being taken to establish a peaceful life."

-ABC News Christina Theodorou