The move came amid fears of a Russian invasion after Russian forces seized three Ukrainian vessels and 24 sailors in the Black Sea last Sunday.
The upper chamber approved the resolution by unanimous consent late Thursday, hours after Trump announced on Twitter he was canceling a meeting with Russian President Vladimir Putin that had been scheduled for Saturday in Buenos Aires.
His comments came after intense telephone diplomacy on November 28 which saw Erdoğan hold talks with Russian President Vladimir Putin and Ukrainian counterpart Petro Poroshenko.
He was referring to Russian-backed separatists who formed units in April 2014 to fight Ukrainian government forces in eastern Ukraine.
Moscow insists Ukraine were illegally entering the waters - something Kiev strongly refutes, saying prior notice was given.
Ukraine had sought the Ecumenical Patriarchate's consent to establish an independent church and won its backing in October, prompting the Russian Orthodox Church to break off diplomatic ties with the Istanbul-based Patriarchate.
Poroshenko said sending North Atlantic Treaty Organisation ships would send a clear message to Putin.
Russia refuses to deescalate: Russian military deploys missiles to border and parades captured Ukrainians on TV
Spokesman of the General Staff Vadym Skybitsky explained that the image is supposed to show the possible extent of Russian military aggression in the Azov and the Black Sea region.
"We are dismayed at this use of force by Russian Federation which, against the backdrop of increasing militarisation in the area, is unacceptable", European Union foreign policy chief Federica Mogherini said.
The strait also separates Russian Federation from Crimea, the peninsula Moscow illegally annexed from Ukraine four years ago.
Russia is calling on the United Nations, the OSCE, the Council of Europe and other worldwide organizations to pay attention to violations of human rights in that country, Russian Foreign Ministry spokesperson Maria Zakharova said on Friday.
Peter Tsigikal, the head of the state border service of Ukraine, told the president that his department was on the highest level of combat readiness, security measures were boosted on the border with Russia and the Russian-annexed Crimean peninsula.
Mr Putin accused his Ukrainian counterpart of provoking the naval incident in a bid to use martial law to shore up his sagging popularity and sideline competitors ahead of the March election.
Asked about the Turkish offer, Peskov responded that "Moscow is grateful to all those willing to help de-escalate the tensions provoked by the Ukrainian side, but doesn't see any need for mediation efforts". So far, the West has offered condemnations of Russia's attack on Ukrainian ships but made no move to sanction Russian Federation. The vessels were trying to pass through the Kerch Strait on their way to the Sea of Azov.
Russian warships fired at the Ukrainian vessels and rammed the tug.
The state security service was investigating him under an article in the criminal code covering "violations of citizens' equality depending on racial ethnicity, religious convictions, incitement of inter-confessional hostility", SBU official Ihor Huskov said.More news: 145 pilot whales die after stranding on New Zealand beach