President Vladimir V. Putin of Russia laid the groundwork on Saturday for blaming Ukraine for the Moscow concert hall attack. And in making his first remarks on the assault more than 19 hours after it began, he pledged to punish the perpetrators, “whoever they may be, whoever may have sent them.”

Mr. Putin, in a five-minute televised address, claimed that someone in Ukraine had tried to help the attackers escape across the border from Russia before they were apprehended by Russian security services.

He did not definitively pin the attack on Ukraine; nor did he refer to the assessment by American officials that a branch of the Islamic State was behind it.

“They were trying to hide and were moving toward Ukraine,” Mr. Putin said, referring to the four men who carried out the attack and who the Kremlin said had been captured in western Russia. “Based on preliminary information, a window for crossing the border was prepared for them by the Ukrainian side.”

Ukrainian officials have repeatedly denied having anything to do with the attack, and American officials have said there is no evidence of Ukrainian involvement. American officials voiced concern on Friday that Mr. Putin could seek to falsely blame Ukraine for the attack, and some analysts and Kremlin critics have said that he could use such an accusation to justify another escalation in Russia’s invasion.

Mr. Putin has in the past blamed the West for stoking terrorist groups to commit violence inside Russia, but he did not refer to the United States or the West in Saturday’s speech. Nor did he mention the March 7 security alert issued by the United States Embassy in Moscow about the risk of attacks on concerts in the Russian capital, which pro-Kremlin figures have used as evidence of possible American complicity.

“We are counting here on cooperation with all countries that genuinely share our pain and are ready, in their deeds, to truly unite our efforts in the fight against the common enemy of international terrorism,” Mr. Putin said.

He declared Monday a national day of mourning and said that security measures were being tightened across Russia.

“The main thing now is to prevent those who were behind this bloody massacre from committing new crimes,” Mr. Putin said.