EU statement came as Russia-led troops arrived in Kazakhstan to help quell mass unrest that left dozens dead and hundreds detained.
The European Union has called on Russia to respect Kazakhstan's sovereignty and independence.
The call came as Russia sent in paratroopers to quell an uprising after deadly violence spread across the former Soviet republic.
"The violence must be stopped. We are also calling for restraint from all parties and a peaceful resolution of the situation," an EU spokesperson said on Thursday.
"Now obviously, the EU is ready and willing to support a dialogue in the country."
Meanwhile, fighting appeared to be continuing a day after protesters stormed several government buildings.
Security forces in Kazakhstan killed dozens of protesters trying to storm government buildings overnight.
In the worst reported violence so far, police on Thursday said dozens of people were killed in battles with security forces at government buildings in the country's largest city Almaty.
"Last night, extremist forces tried to assault administrative buildings, the Almaty city police department, as well as local police commissariats. Dozens of assailants were eliminated," police spokesman Saltanat Azirbek was quoted as saying by the Interfax-Kazakhstan, TASS and Ria Novosti news agencies.
Videos on social media on Thursday showed pillaged shops and burned buildings in Almaty, automatic gunfire in the streets and residents screaming in fear.
Kazakhstan's Health Ministry said more than 1,000 people have been wounded in days of mounting unrest in Kazakhstan.
Long seen as one the most stable of the ex-Soviet republics of Central Asia, energy-rich Kazakhstan is facing its biggest crisis in decades after days of protests over rising fuel prices escalated into widespread unrest.
Troops sent on Kazakh request
Meanwhile, a Moscow-led military alliance said on Thursday it had sent its first troops to Kazakhstan after its government requested help to quell mounting unrest.
"Peacekeeping forces of the Collective Security Treaty Organisation were sent to the Republic of Kazakhstan for a limited time to stabilise and normalise the situation," the CSTO secretariat said in a statement posted online by Russian Foreign Ministry spokeswoman Maria Zakharova.
The deployment came in response to an appeal from the president of Kazakhstan to help stabilise the Central Asian country amid a wave of protests sparked by a fuel price rise.
The statement did not specify how many troops were being sent but said the Russian contingent included members of the country's Airborne Forces.
Protests spread across the nation of 19 million this week in outrage over a New Year's Day increase in prices for liquid petroleum gas (LPG), which is widely used to fuel cars in the west of the country.
Thousands took to the streets in Almaty and in the western province of Mangystau, saying the price rise was unfair given oil and gas exporter Kazakhstan's vast energy reserves.
With protests escalating, the government late on Wednesday said a state of emergency declared in protest-hit areas would be extended nationwide and in effect until January 19.
The EU and the UN called for "restraint" on all sides, while Washington urged authorities to allow protesters to "express themselves peacefully."