The EU will not accept a "veto" by Russia on the bloc's ties with former Soviet republics, European Commission President Jose Manuel Barroso has said.
Speaking at an EU meeting in Lithuania, Mr Barroso said the era of "limited sovereignty was over in Europe".
The summit failed to revive an association agreement with Ukraine that was due to be its centrepiece.
Ukraine's president said he could not afford to sacrifice trade with Russia - which opposes the deal - for EU ties.
Many Ukrainians nevertheless protested against the decision.
In the capital, Kiev, thousands of demonstrators draped in Ukrainian and EU flags and chanting "Ukraine is Europe" formed a human chain from Independence Square along the main street of Khreshchatyk.
The protesters said they would demand the resignation of the Ukrainian government and the President, Viktor Yanukovych, and would seek his impeachment. They also promised mass protests across the country.
"Europe was the way out of the mess we're in, the way out of the corruption that has overwhelmed our country," Andrey Dobrolet, a lawyer, told the Reuters news agency. "But now we see the real colours of the people in power."
In the western city of Lviv, about 20,000 joined hands, the AFP news agency reported.
At the same time, thousands of the president's supporters attended a rally in Kiev's European Square, where speakers warned of the dangers of European integration.
President Yanukovych froze plans to sign Ukraine's trade deal last week. In Vilnius, he defended his refusal to sign, saying the EU was not offering adequate financial aid.
After the two-day summit, Mr Barroso said: "We will not give in to external pressure, not the least from Russia.
"What we cannot accept is a condition on a bilateral agreement to have a kind of a possible veto of a third country. This is contrary to all principles of international law."
EU Council President Herman Van Rompuy said the parties had been "really close" to signing the association agreement, but added that "we need to overcome pressure from abroad".
"We are embarked on a long journey, helping Ukraine to become, as others, what we call now, 'new member states'. But we have to set aside short-term political calculations."
However progress was made with two other ex-Soviet states, Georgia and Moldova.
Association agreements with both were initialled - a stage prior to signing - on Friday. Diplomats have expressed hope those deals can be signed next year.
EU leaders said in a statement earlier that they "strongly" disapproved of Moscow's pressure on Ukraine not to sign - while Russian President Vladimir Putin accused the EU of "blackmail".
Analysts say Russia worked hard to undermine the EU agreement with Ukraine, which it sees as a strategically vital partner.
On the one hand, it offered Kiev loans and price discounts. On the other, it threatened painful trade sanctions and higher gas bills.
In comments reported on his website on Friday, President Yanukovych said Ukraine still intended to sign an association agreement, but that were "several crucial steps left to be made".
He stressed that these would include a "programme of joint measures aimed at the adaption of the Ukrainian economy to the new realities" and to minimise "negative consequences" for the most vulnerable groups.
Mr Yanukovych has previously described an EU offer to lend Ukraine 610m euros (£510m; $828m) as inadequate, and said that his country would need at least 20bn euros a year to cover the cost of upgrading its economy to "European standards".
Prominent Ukrainian opposition politician Vitali Klitschko, who attended the Vilnius summit before flying back to speak to the protesters in Kiev, also said he hoped an agreement would eventually be signed.
"We Ukrainians want the changes," the world boxing champion added. "We want to live with the European family, with European rules, with Europeans' life standards."