Trump plays down chances of quick breakthrough as N. Koreans bring letter

(Adds Kim quote, paragraph 6, details on Trump's comments)

* Trump says several North Korea meetings may be needed

* North's leader Kim sends envoy with letter for U.S. president

* Kim tells Lavrov, position "unchanged, consistent and fixed"

* U.S. top diplomat in talks with North Korea official

By Yara Bayoumy and Steve Holland

NEW YORK/ABOARD AIR FORCE ONE, May 31 (Reuters) - U.S. President Donald Trump on Thursday played down the chances of a quick deal to get North Korea to abandon its nuclear weapons as a delegation from Pyongyang headed to meet him with a letter from North Korean leader Kim Jong Un, suggesting a proposed summit may be back on.

Trump told Reuters he was still hoping for an unprecedented meeting with Kim on June 12 in Singapore to push for North Korean "denuclearization," although he conceded it might require more time to reach that goal.

"I’d like to see it done in one meeting," Trump said in an interview on Air Force One. "But often times that’s not the way deals work. There’s a very good chance that it won’t be done in one meeting or two meetings or three meetings. But it’ll get done at some point."

North Korea has rejected previous U.S. calls for its unilateral nuclear disarmament and argued instead for a "phased" approach to denuclearization of the entire Korean peninsula, which in the past has also meant removal of the U.S. nuclear umbrella protecting South Korea and Japan.

In Pyongyang, Kim said his country's will to see denuclearization on the Korean peninsula remained "unchanged, consistent and fixed,” but said he hoped that and improved North Korea-U.S. relations would both be solved on a "stage-by-stage" basis.

Kim said he hoped to find a “solution to meet the interests of each other through a new method in a new era and under a new situation and the solution of the issues will progress through effective and constructive dialogue and negotiation,” the official Korean Central News Agency said.

Kim made the remarks in a meeting with Russian Foreign Minister Sergei Lavrov and the two men also agreed their countries should hold a bilateral summit this year.

Until this year, Kim had made no visits outside his country since taking over from his father as leader in 2011.

But he has had two summit meetings in recent weeks with South Korea and made two visits to China as part of a campaign of diplomatic outreach aimed at easing Pyongyang's isolation and U.S.-led international sanctions.

U.S. Secretary of State Mike Pompeo said a North Korean delegation, headed by high-ranking official Kim Yong Chol, with whom he held two days of talks with in New York, would make a rare visit to the White House on Friday and give Trump a letter from Kim.