Sunday's incident has sparked worldwide condemnation over Russia's use of force.
The strait is spanned by a new bridge that Russia completed this year - the only land link from the Russian mainland to the annexed peninsula of Crimea.
"Let's be clear about what is known: Ukrainian ships set sail from one Ukrainian port to another Ukrainian port", Haley said.
While a 2003 treaty designates the Kerch Strait and Sea of Azov as shared territorial waters, Moscow has sought to assert greater control over the passage since the annexation.
NATO Secretary General Jens Stoltenberg pledged the alliance's "full support for Ukraine's territorial integrity" following a phone call with Ukrainian President Petro Poroshenko on Monday morning. "It is introduced with the sole goal of boosting Ukraine's defence in the light of a growing aggression from Russian Federation".
However, after the annexation of the Crimean peninsula by Russia in 2014, which violated several bilateral agreements between the two countries in addition to worldwide law, Western nations have protested increasing Russian control, which some media call "creeping annexation".
Angrily. Ukraine called the attack on the ships an "act of aggression" and parliament voted to declare martial law in border territories, a measure it resisted even at the worst moments of the conflict in south-east Ukraine.
"We consider it as an act of aggression against our state and a very serious threat", he said.
ASSOCIATED PRESS President Petro Poroshenko addresses the Ukrainian parliament
Critics of Poroshenko say that instituting martial law could be a tactic of the current Ukrainian president to postpone an election that he is in danger of losing. Sunday's conflict, Moscow says, was "thoroughly planned and orchestrated" to distract Ukrainians from domestic problems ahead of their March 2019 presidential election.
The number of Russian units deployed along the Ukraine-Russian border has "grown dramatically" while the number of Russian tanks has tripled, Poroshenko said, citing intelligence reports but giving no precise timescale for the buildup.
Several countries have condemned Russia's actions on Monday, and the UN Security Council failed to agree a Russian-proposed agenda, and instead discussed a Ukrainian proposal on the issue.
The Ukrainian ships were passing into the Sea of Azov, which is linked to the Black Sea by the narrow Strait of Kerch, when they were blocked by a Russian tanker.
It said the Ukrainian action was coordinated with the United States and the European Union to "create a pretext to ramp up sanctions against Russia".
Russian President Vladimir Putin informed German Chancellor Angela Merkel that he is "seriously concerned" about the growing tensions between the two countries after the weekend incident and Ukraine's instituting martial law.
Meanwhile, US President Donald Trump told reporters outside the White House Tuesday that he was "not happy about it at all", but refused to take the belligerent stance his United Nations envoy, Nikki Haley, adopted the previous day.
Ukraine said its vessels were heading to the Sea of Azov in line with worldwide maritime rules, while Russian Federation said they had failed to obtain permission to pass through the narrow strait that is spanned by a 11.8-mile bridge that Russian Federation completed this year. "We're all working on it together", Trump told reporters. And hopefully they'll get straightened out.
The Kremlin on Tuesday warned that Ukraine's declaration of martial law in border and coastal areas could lead to a flare-up of hostilities in the country's conflict-ridden eastern provinces.
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