The governor of Lviv, in the west, was forced to sign his resignation as protesters stormed his offices.
Other reports spoke of protests in at least five more western cities.
Two people died in clashes in Kiev on Wednesday, the first deaths in two months of protests over EU links.
The anti-government protests flared in late November over Mr Yanukovych's decision to pull out of a landmark treaty with the European Union.
A fragile truce is currently being observed in Kiev.
However, an opposition ultimatum is set to expire after the talks with Mr Yanukovych, which have now begun and are set to go into the evening.
Ahead of the talks, Mr Yanukovych asked the speaker of parliament to hold an emergency session next week to discuss the crisis.
But he told the head of the European Commission, Jose Manuel Barroso, that he would not introduce a state of emergency.
Prime Minister Mykola Azarov, who is in Davos in Switzerland, echoed this, but added: "People should not think that the government lacks available resources to put an end to this. It is our constitutional right and obligation to restore order in the country." (+ BBC videos) » | Thursday, January 23, 2014
