Aksyonov arrived at the upscale Oberoi hotel accompanied by Russian diplomats to be greeted by a Mumbai-based merchant who wants to boost trade with Russia.
Russia has denied Ukrainian and Western allegations that it is fomenting the rebellion by sending troops and weapons into Ukraine.
The new resolution includes parts of two earlier resolutions it circulated this month which called for humanitarian aid, a cease-fire, and a national dialogue in Ukraine.
The European Commission said in a statement Monday that Ukraine was ready to accept a compromise in talks in Kiev of paying $1 billion now and more later, but Russia was not.
Few events illustrate more clearly the bitter chasm that has opened up between east Ukraine and the rest of the country of 45 million.
Ukrainian Interior Minister Arseny Avakov said the tanks had rolled across the border from Russia, but rebels said they were from a Ukrainian military stockpile.
It was a bitter setback for Ukrainian forces, which have struggled to suppress an armed insurgency by foes of the new government.
Any indication they came from Russia would be likely to deepen strains between Moscow and the West over the Ukraine crisis
In an advisory, it also asked citizens in the other parts of eastern and southern Ukraine to remain vigilant about their personal safety and security.
The targets of the new sanctions include Russia's top prosecutor in Crimea; commander of Russian airborne troops; a member of Putin's staff, among others.
The Kremlin also urged the Organization for Security and Cooperation in Europe to help broker talks between the central government in Kiev and representatives of the east after Sunday's vote.
President Vladimir Putin's spokesman said the Kremlin was "extremely worried" that it had not heard from an envoy Putin had sent to the eastern city to help free foreign hostages.
Obama announced the sanctions during a news conference in the Philippines, his final stop on a four-country Asia swing.
Ukrainian forces killed up to five pro-Moscow separatists in the east of the country on Thursday.
Ukraine said the drive to root the separatists out would continue and warned it could take "more concrete actions" next week if they do not back down.
Enacting the agreement on the ground though will be difficult, because of the deep mistrust between the pro-Russian groups and the Western-backed government in Kiev
A crowd of around 300 men armed with Molotov cocktails attacked the base, in the south-east part of the country late Wednesday, Interior Minister Arsen Avakov said in a statement.
Tensions continued to mount ahead of high-level diplomatic talks on the Ukraine crisis in Geneva on Thursday after Kiev sent in troops to oust pro-Moscow separatists from the east.
The government in Kiev has struggled to reign in the rebels, as some security forces have switched over to the side of the insurgents.
Putin told German Chancellor Angela Merkel in a telephone call late on Tuesday that Kiev had "embarked on an anti-constitutional course" by using the army against the rebels.