Amid the recent tensions, the United States notified Turkey that two US warships would sail to the Black Sea on April 14 and April 15 and stay there until May 4 and May 5.
Kuleba was to hold talks in Brussels later Tuesday with US Secretary of State Antony Blinken, who has jetted back for fresh talks at North Atlantic Treaty Organisation after a visit last month.
"If there is any aggravation, we of course will do everything to ensure our security and the safety of our citizens, wherever they are", Deputy Foreign Minister Sergei Ryabkov was quoted as saying by Russian news agencies.
Stoltenberg stressed that the alliance - not Moscow - will choose whether Ukraine joins NATO: "It is for the 30 NATO allies to decide when Ukraine is ready for NATO membership, and no one else has any right to try to meddle or to interfere in that process".
Ryabkov's remarks suggest that the diplomatic niceties which the former Cold War enemies have generally sought to observe in recent decades is fraying, and that Russian Federation would robustly push back against what it regards as unacceptable USA interference in its sphere of influence.
We, the G7 foreign ministers of Canada, France, Germany, Italy, Japan, the United Kingdom and the United States of America and the High Representative of the European Union are deeply concerned by the large ongoing build-up of Russian military forces on Ukraine's borders and in illegally-annexed Crimea. "We warn the USA that it should stay away from Crimea and our Black Sea coast for their own benefit".
"Russia must end this military build-up in and around Ukraine, stop its provocations and de-escalate immediately", Stoltenberg said at a news conference with Kuleba.
Russian Federation has not denied the troop buildup along the border but officials said it was not planning on going to war with Ukraine.
US Secretary of State Antony Blinken is scheduled to hold talks with Kuleba.
"In total, 40,000 troops and 15,000 weapons and pieces of military equipment are concentrated near our territory, including strategic aircraft", Shoigu said.
Russian Federation and Ukraine have traded accusations about the increasing tensions in the eastern Donbass region.
Kuleba called for further economic sanctions on Russian Federation and more military support for Ukraine.
"At the operational level, we need measures which will deter Russian Federation and which will contain its aggressive intentions", Kuleba said after the NATO-Ukraine Commission met at the alliance headquarters.
Stoltenberg's comments came ahead of an emergency meeting of allied foreign and defense ministers over the conflict in the eastern Ukraine region. "The United States is committed to rebuilding US alliances, particularly with our NATO Allies", Blinken Tweeted on Monday.
Ukraine is on a diplomatic blitz this week, trying to garner support for its position.