Guterres underscored "the need to fully respect the rights and obligations of all concerned parties" under global law and said "the sovereignty and territorial integrity of Ukraine, within its internationally recognized borders. must also be fully respected".
Ukrainian President Petro Poroshenko has said that he will ask the Ukrainian Parliament to impose martial law. The decision is meant to put troops at a higher state of combat readiness for 30 days in areas where Ukraine shares a border with Russian Federation.
The two neighbors have been locked in a tense tug-of-war since Russia's 2014 annexation of Crimea, but the incident late on Sunday in which Russian coast guard ships fired on Ukrainian navy vessels near the Kerch Strait directly pitted the two militaries, placing them on the verge of an open conflict.
However, a Russian ship blocked their passage, took control of the ships and seized the crews.
"The US should provide Ukraine with military assistance that is defensive in nature, for example radars, intelligence, surveillance and reconnaissance assets for maritime domain awareness, I would say land-base anti-ship missiles for defense of Ukraine Azov sea littoral", explained Michael Carpenter, expert from the Atlantic Council.
On Tuesday, Kremlin spokesperson Dmitry Peskov said Ukraine's decision to introduce martial law had a "barely camouflaged" political agenda, although he added that the move was an internal matter for Kiev.
The clash comes as Ukrainian forces are fighting Russia-backed separatists in eastern Ukraine in a conflict that has killed more than 10,300 people since April 2014.
Martial law would allow Ukraine to respond swiftly to any invasion and mobilise resources as quickly as possible, he said.
"Russian coastguard vessels ... carried out openly aggressive actions against Ukrainian navy ships", Ukrainian authorities said in a statement, revealing that the tugboat's engine, hull, railings, and lifeboat were damaged in the incident.
TASS reported the three Ukrainian vessels were detained by Russian forces and that "weapons were used to force them to stop". One of them was clearly reading from a script prepared for them.
After the incident, Russian media accused Ukraine of staging a "provocation" and violating Russia's borders.
Ukraine said six of its servicemen were injured in the incident, two seriously. "At the same time, we have to work for de-escalation".
But Ukraine's foreign minister, Pavlo Klimkin, said "Ukraine will seek to settle the row in a peaceful manner", even though its armed forces have been put on alert. A court Tuesday in the Crimean capital of Simferopol ordered one of the Ukrainian seamen to be kept behind bars until January 26.
The court hearings took place in Simferopol, the main city in Crimea, and are expected to continue on Wednesday.
The attack by the Russian Coast Guard on Sunday occurred as the three Ukrainian ships attempted to pass from the Black Sea through the Kerch Strait off eastern Crimea into the Sea of Azov for access to Ukrainian ports.
In a phone conversation with German Chancellor Angela Merkel, Mr Putin expressed "serious concern" over the introduction of martial law, the Kremlin said in a statement. He spoke after meeting with French Foreign Minister Jean-Yves Le Drian, who appeared to soften his criticism of Moscow.
In the evening on 25 November, Ukrainian vessels with 23 crew members been fired on and seized by the Russian troops in global waters.
Ukrainian Foreign Minister Pavlo Klimkin tweeted that the dispute was not an accident and that Russia had engaged in "deliberately planned hostilities", while Russian Foreign Minister Sergey Lavrov blamed Kiev for what he described as a "provocation", adding that "Ukraine had undoubtedly hoped to get additional benefits from the situation, expecting the USA and Europe to blindly take the provocateurs' side".