KYIV, Ukraine—President Vladimir Putin of Russia said the U.S. and its European allies had “basically ignored” Moscow’s demands for security assurances but expressed a willingness to continue talks as Russian troops maneuvered near Ukraine’s borders and Kyiv rushed to bolster its defenses.

“We didn’t see an adequate response to our key concerns,” Mr. Putin told reporters Tuesday at a Kremlin press conference at which he again castigated the North Atlantic Treaty Organization for what he has portrayed as a persistent eastward push that threatens Moscow.