Ukrainian Prime Minister Arseniy Yatsenyuk has vowed Ukraine would not give "an inch" of its territory to Russia, at a rally of thousands of people in Kiev in honour of 19th-century national hero Taras Shevchenko.
"This is our land. We will not give an inch of it. Russia and its president should know that," Yatsenyuk said on Sunday after Russian forces and pro-Kremlin gunmen seized control of Ukraine's Crimea peninsula in the Black Sea.
Yatseniuk will visit Washington this week for talks as tensions build over Russian forces' seizure of the Crimea, a White House official confirmed on Sunday. No other details about the talks were immediately available from Washington officials.
"I am going to the US for meetings at the highest level aimed at settling the situation in Ukraine," Russia's Interfax news agency quoted Yatsenyuk as telling a government meeting.
The developments come as clashes erupted between pro-Ukrainians and pro-Russians at Sevastopol, AFP news agency reported.
In Simferopol, hundreds gathered at a pro-Russia rally in front of a statue of Lenin.
Protester Vasiliy Bulahov told Al Jazeera he did not think Ukraine's government was legitimate. "We are Russian and... Russia and Crimea [are] together forever," he said.
Trouble in the ex-Soviet state has continued as the government struggles to contain upheaval amid a standoff between Russia and the West over Crimea that shows no sign of easing.
Sunday marks 200 years since the birth of Ukraine's national hero, the poet Taras Shevchenko, and patriotic rallies were held in Kiev and - in a show of defiance of Russia's de facto control over Crimea - the peninsula's key cities of Simferopol and Sevastopol.
Pro-Russian protesters held a counter-rally in the tense eastern city of Donetsk, where clashes were feared between them and pro-Kiev demonstrators also planning to celebrate Shevchenko.
The internal wrangling over Ukraine's identity and future were mirrored on the international stage by escalating hostilities between Russia and the West.
Russian forces tightened their grip on Crimea on Sunday despite a US warning to Moscow that annexing the southern Ukrainian region would close the door to diplomacy in a tense East-West standoff.
Russian forces' seizure of the Black Sea peninsula has been bloodless but tensions are mounting following the decision by pro-Russian groups that have taken over the regional parliament to make Crimea part of Russia.
In the latest armed action, Russians took over a Ukrainian border post on the western edge of Crimea at around 6am (04:00) GMT, trapping about 30 personnel inside, a border guard spokesman said.
The spokesman, Oleh Slobodyan, said Russian forces now controlled 11 border guard posts across Crimea, a former Russian territory that is home to Russia's Black Sea fleet and has an ethnic Russian majority.
On Saturday, pro-Kremlin militia fired warning shots to stop foreign observers from entering Crimea, and Moscow threatened to suspend its participation in nuclear arms monitoring deals.
It was the third straight day that civilian and military observers from the Organisation for Security and Co-operation in Europe (OSCE) tried and failed to enter the Black Sea peninsula to check on the standoff between overpowered Ukrainian troops and a mass of Russian forces and Kremlin-backed militias.
The OSCE monitoring mission is an instrumental part of a three-pronged diplomatic push by US President Barack Obama that also includes a call for Russia to pull its Crimean troops back to their barracks and Ukraine to hold early presidential polls in May.