He said he would decide on a course afterward.
Ms Sanders said that the USA and Russian governments had exchanged phone calls. He stopped short of condemning Russian Federation, instead saying: "I don't like that aggression".
White House spokeswoman Sarah Sanders told reporters on the presidential aircraft that Trump made the decision not to meet Putin after speaking with Secretary of State Mike Pompeo, White House chief of staff John Kelly and national security adviser John Bolton.
Russian Federation and Ukraine have been at loggerheads since 2014 when Russian Federation annexed Crimea after a controversial referendum.
The Russians then captured the ships and their crews. A decision on the rest was expected yesterday. At least three of the men are in hospital.
The Ukrainian parliament on Monday voted in favour of Poroshenko's request for martial law, which gives authorities the power to mobilise citizens with military experience, regulate the media and restrict public rallies in affected areas.
The discussions with Moscow continued over the next five months, culminating in an invitation from Peskov's office for Cohen to attend the St. Petersburg Forum in June 2016, where Cohen would be introduced either to Putin or to Prime Minister Dmitry Medvedev.
He insisted Russia's military response was appropriate as the Ukrainians had "trespassed" into Russia's territorial waters.
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A long-planned meeting between the United States and Russian presidents was called off suddenly on Thursday, shortly after President Trump's former personal lawyer pleaded guilty to lying to Congress about Trump business dealings with Russia.
On the ground for just two days, Trump is packing every moment with diplomacy, conducting bilateral meetings with numerous world leaders as well as group events.
But Russian officials said that the situation in Ukraine wasn't the real reason that Trump opted to cancel the much-anticipated meeting with Putin.
"It is wrong to assume that the Russian side needs this meeting more", Konstantin Kosachev, head of the Russian Federation Council's International Affairs Committee, said on Facebook. Germany, too, has to ask itself: "What will Putin do next if we do not stop him?"
'A vicious practice of returning to illegal, unilateral sanctions and protectionist measures is spreading, going around the UN Charter, the rules of the WTO and internationally recognized legal norms, ' Putin said.
Trump, who has been accused of being soft on Russian and President Putin, has been under pressure to punish Russia for attacking Ukrainian ships and capturing their sailors.
"I can say that there was a request, but a conversation did not take place, so to speak", Kremlin aide Yuri Ushakov said. However, during the exit from the Kerch Strait, the Russian border guard vessel opened fire on Ukrainian ships, in result, 6 Ukrainian soldiers were injured.
Western governments have backed the Ukrainian government.