By Natalia Zinets and Steve Holland

KIEV/NEW YORK (Reuters) - Ukraine's Petro Poroshenko met U.S. President Donald Trump on Thursday and said afterwards that they had a shared vision on a "new level" of defense cooperation, but not whether this included the U.S. provision of defensive weapons to Ukraine.

The United States is reviewing whether to send weapons to Ukraine to help it defend itself, an option that previous U.S. president Barack Obama vetoed and which is opposed by Russia.

After meeting Trump in New York, President Poroshenko told a televised briefing: "It's very important that there is a shared vision on a new level of cooperation in the defense sphere."

"We discussed all areas of this cooperation, including cooperation with the defense ministry and other institutions," he added, without saying whether there had been any progress on the defensive weapons initiative.

The two leaders skirted around the topic of Russia when they spoke to reporters at the beginning of their private meeting.

Instead, they chose to emphasize economic cooperation when they appeared before reporters at their meeting on the fringes of the U.N. General Assembly.

Relations between Kiev and Moscow are at their lowest ebb since Russia annexed Crimea more than three years ago and Russian-backed separatist fighters took up arms against Ukrainian government forces in the east of the country.

Before holding private talks, Trump praised Poroshenko, telling him that "I wouldn't say it's (Ukraine) the easiest place to live" but "it's getting better and better on a daily basis."

Speaking in English, Poroshenko said he believed that the two countries had improved security and economic cooperation with many U.S. companies doing business in Ukraine.

"That's a story that's pretty untold," said Trump. "Companies are going very strongly right now into the Ukraine, they see a tremendous potential there."

It was not immediately clear if they spoke privately about relations with Russian President Vladimir Putin, who did not attend the U.N. General Assembly.

The war in eastern Ukraine between pro-Russian separatists and Ukrainian government forces has killed more than 10,000 people in three years. Kiev accuses Moscow of sending troops and heavy weapons to the region, which Russia denies.

Poroshenko said Trump had supported Ukraine's proposal to deploy U.N peacekeepers "including on the uncontrolled part of the Ukraine-Russia border, which would prevent the possibility of penetration by Russian troops or Russian weapons".

Putin this month also suggested U.N. peacekeepers be deployed to eastern Ukraine.

But Russia has balked at Ukraine's proposal that would ban any Russian nationals from taking part in the peacekeeping mission which Kiev wants deployed along the part of its border with Russia it does not control.

Poroshenko said the meeting with Trump lasted an hour and was also attended by U.S. Vice President Mike Pence, Secretary of State Rex Tillerson and other senior U.S. officials.

(Writing by Alessandra Prentice and Steve Holland; Editing by Catherine Evans and James Dalgleish)