(CNN) -- The European Union can help resolve some of the financial concerns that have prevented Ukraine from signing a landmark trade deal, its top diplomat said Monday, as tens of thousands of protesters kept up demonstrations over fears that Kiev would be moving closer to neighbor Russia.
EU foreign policy chief Catherine Ashton told reporters in Brussels, Belgium, that she believed the bloc could work with Ukrainian President Viktor Yanukovych on Kiev's concerns after the Eastern European country backpedaled on signing the Association Agreement.
Her comments came just hours after Stefan Fule, European commissioner for enlargement and European neighborhood policy, said on Twitter that efforts were being halted amid growing doubts that any deal could be done with Kiev.
"We are very concerned when we look at some of the things that are being said, and my purpose in talking to President Yanukovych was to discover what these short-term economic issues are that have prevented him from signing," Ashton said ahead of an EU foreign ministers meeting.
"I feel that we can work with him to resolve those. Some of them can be done through the support of the European Union, others through financial institutions, some of them through the private sector. All of them are possible."
After months of talks, Yanukovych in November spurned the EU agreement in favor of closer economic ties with Moscow, sparking mass protests in Kiev that have paralyzed the city center.
The demonstrators have stood their ground, camping out in freezing temperatures in Independence Square, or Maidan, and barricading surrounding streets.
They were out in the tens of thousands Sunday -- the fourth weekend in a row -- urging their leaders to mend ties with Brussels.
Yanukovych is due to travel to Moscow on Tuesday. There, Ukraine and Russia plan to approve a road map to improved trade relations, Prime Minister Mykola Azarov said Sunday in a late-night interview on Ukraine's national broadcaster, Inter TV.
Azarov also said he hoped an agreement could be reached on gas commerce, which would hopefully provide a solution for Ukraine's unprofitable gas transportation system.
However, he rejected claims that Ukraine is leaning toward joining Russia and other former Soviet republics in a Customs Union.
"These are speculations. None of the papers we have prepared are in any way related to the Customs Union," he said.
Frustration in Brussels
Ashton traveled to Kiev last week, where she said Yanukovych had assured her of his intent to sign the EU deal.
That was no longer clear a few days later, according to officials in Brussels.
On Sunday, Fule said on Twitter that the words and deeds of Yanukovych and his government on the proposed pact were "further & further apart. Their arguments have no grounds in reality."
Fule said he had told Ukrainian Deputy Prime Minister Serhiy Arbuzov in Brussels last week that further discussion of the agreement was conditional on a clear commitment by Kiev to sign the deal, but he had received no response.
The EU Foreign Affairs Council is expected Monday to discuss the events in Ukraine, where the constant mass protests have plunged the nation of 45 million people into a political crisis.
Russian Foreign Minister Sergey Lavrov will attend a working lunch with his European counterparts there.
"I don't believe that the crisis in Ukraine should have a negative impact on our relations with Russia," Ashton said. "It does mean though that we have to look very seriously about the way in which countries make their decision and are entitled to make their decision."
Ukraine, a key transit region for Russian gas going to Western Europe, desperately needs a cash injection.
Azarov last week told a government meeting that Ukraine was still open to signing the European integration deal, if the European Union would agree to provide financial assistance to Ukraine of around 20 billion euros ($27.5 billion).
A statement on the presidential website Monday said Yanukovych "emphasized the invariability of the European integration course of Ukraine and the faithfulness to national interests of the state."
He said this during a meeting with U.S. Sens. John McCain and Chris Murphy, who on Sunday addressed the protesters occupying Independence Square.
The anti-government demonstrations are the biggest since the Orange Revolution overturned the results of Ukraine's 2004 presidential election.
McCain, who traveled to Kiev on the weekend, met with opposition leaders Saturday before taking to the stage Sunday.
"Ukraine will make Europe better, and Europe will make Ukraine better," he told the protesters, who replied with roaring chants of "Thank you."
The daily rallies have been growing in size in the evening, when people finish work. A police crackdown last week -- condemned by Western governments -- has fueled anti-government support.
But there have also been pro-government demonstrations in the last few days.
The presidential statement said Yanukovych had "assured that the government made everything possible to ensure the rights of citizens to peaceful demonstrations" and had allowed for an investigation into the violence that erupted on the streets late last month.
Ukrainian prosecutors are investigating some top government officials over the beating of students at anti-government protests two weeks ago.
The subjects of the criminal investigation include Ukrainian Deputy Secretary for National Security Vladimir Sivkovich, Kiev Police Chief Valery Koryak and Kiev Mayor Oleksandr Popov. A fourth person also is under investigation.
The case will be put before a judge Monday, who could order house arrest for those being investigated, said Valery Vilkova, a spokeswoman for the general prosecutor.
The tumult in Ukraine goes to the heart of its future ties with Russia and the rest of Europe.
Ukraine is split between pro-European regions in the west and a more Russia-oriented east.
The protests have unfolded since November 21, when Yanukovych changed his stance on the EU trade pact, which had been years in the making.
The demonstrators say an EU agreement would open borders to trade and set the stage for modernization and inclusion.
CNN's Antonia Mortensen contributed to this report.