The American and European offers are also intended to answer political criticism in Washington and some European countries that the West is not doing enough to support Ukraine in the face of Russian threats.

European Union leaders will meet on Thursday in Brussels to consider sanctions against Russia. The loan announcement on Wednesday came from José Manuel Barroso, president of the European Commission, the union’s executive arm. He said the offer of 11 billion euros, or $15 billion, “over the next couple of years” included €1.6 billion, or about $2.2 billion, in loans and €1.4 billion in grants, as well as €3 billion in new credit from the European Investment Bank through 2016.

He also promised efforts with the European Bank for Reconstruction and Development, where the European Union is a majority shareholder, to free up €5 billion, and other steps to grant €3.5 billion in loans.

But Mr. Barroso was vague on the details, indicating a rapid effort to come up with an offer that could come close to matching the original Russian one. He said he would discuss details on Thursday with Ukraine’s interim prime minister, Arseniy P. Yatsenyuk, who will attend the emergency summit meeting of leaders.

The European Union also announced that it was freezing the financial assets in Europe of 18 people held responsible of misusing state funds in Ukraine. Their identities were withheld pending the official publication in the union’s legal journal on Thursday.

In Kiev, Mr. Yatsenyuk said Russia’s deployment of forces was having an “extremely negative” impact on the country’s shaky economy.

But Russia signaled no intention to release its grip on Crimea, headquarters of the Russian Black Sea Fleet. Russian troops there, in uniforms without insignia, continued to surround major Ukrainian military facilities. Most of the Ukrainians have resisted calls to surrender weapons and leave their bases, where they are effectively imprisoned.

In Paris, Mr. Kerry sought to accent the positive. “I personally feel as if I have something concrete to take back and talk to President Obama about so that I can get his input and thinking, advice, on what he’s prepared to do,” he said. “And I believe that Foreign Minister Lavrov is in exactly the same position with respect to President Putin.”