Viktor Yanukovych said a cross-party commission would be set up on Monday to try to resolve the deepening crisis. Opposition leaders confirmed this.
Earlier, a group of protesters – trying to reach parliament – clashed with police. Dozens of people were injured.
The US and EU called for an end to the violence and urgent political talks.
The violence broke out as many thousands of protesters held a rally in Kiev’s Independence Square, outraged by new laws which they said restricted basic freedoms.
The ruling party of Viktor Yanukovych denies this, saying the legislature is in line with European standards.
However, Western countries have expressed deep concern at the new laws.
The anti-government movement began in protest at Viktor Yanukovych’s decision in late November to pull out of a landmark treaty with the EU, but has expanded to demand his resignation.
Late on Sunday, President Viktor Yanukovych’s press office said a “working group” headed by National Security and Defense Secretary Andriy Kluyev would be set up.
It said the group – made of members of government and the presidential administration – would meet opposition representatives on Monday to try to resolve the crisis.
Opposition leader Vitali Klitschko confirmed this after meeting President Viktor Yanukovych at his residence outside Kiev.
“We must use every opportunity to resolve the crisis peacefully,” the former world heavyweight boxing champion, who leads the Udar party, told Ukraine’s Hromadske TV.
He warned against a “scenario of force”, adding that he “didn’t rule out the possibility of a civil war”.
Arseniy Yatseniuk, another opposition leader, said Viktor Yanukovych personally called him to say that he was ready for talks.
However, the opposition warned that the talks must produce real results and not be an opportunity for the president to play for time. The opposition is demanding the resignation of the government and snap presidential elections.
But opposition leaders are under huge pressure to come up with an action plan, amid criticism from many activists that their campaign has been too passive.
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