Tens of thousands of Ukrainian anti-government activists rallied in the capital, Kyiv, as the country's national security agency warned of unspecified threats of terrorism.
About 30,00 opposition supporters turned out for Sunday's rally in Kyiv's Independence Square.
Opposition leaders repeated calls for constitutional reform and new elections that would hopefully unseat President Viktor Yanukovych.
"A new constitution. A new president. A new government. A new country. This is what we want and we will prevail. Glory to Ukraine."
Yanukovych has accepted the resignation of his prime minister and revoked controversial anti-protest laws that angered demonstrators. But the protesters demand more concessions, including Yanukovych's resignation.
Meanwhile Sunday, the State Security Service says it is putting anti-terrorism units on high alert warning that international airports, power stations, and railway and bus stations in major cities were at particular risk.
The agency said in a statement that the anti-terrorism measures would also be applied to blocking of state buildings, in what many see as a warning to demonstrators.
The protests began in November when Yanukovych, under pressure from Moscow, turned down a partnership with the European Union.
The Ukraine government faces severe economic troubles and Russia has promised a $15 billion rescue package. But Russian President Vladimir Putin said last week the funding would not be released in full until a new government is formed in Kyiv.