KYIV (Reuters) - Ukraine and the United States have made "substantial progress" in their talks on a minerals deal and will sign a memorandum in the near future, First Deputy Prime Minister Yulia Svyrydenko said on Wednesday.

U.S. President Donald Trump is seeking a bilateral minerals deal as part of his push to end Ukraine's war against the Russian invasion. Trump also sees it as a way to recover billions of dollars the U.S. has spent on military assistance to Ukraine. President Volodymyr Zelenskiy has said that Ukraine would not recognise past U.S. military aid as loans.

"Our technical teams have worked very thoroughly together on the agreement, and there is significant progress. Our legal staff has adjusted several items within the draft agreement," Svyrydenko said in a social media post on X.

Svyrydenko said the work on the deal would continue and that both sides agreed to sign a memorandum in the near term as the first stage to record the progress.

Deputy Ukrainian Economy Minister Taras Kachka told national television that talks were advancing and that it was likely a provisional document, or memorandum, could be signed very soon.

"A final document won't be signed this week. There is a lot of work to be done because the ideas included in the agreement by the U.S. side need to be developed further," Kachka said.

The United States has reduced its cost estimate for the assistance provided to Ukraine since Russia's invasion in 2022 to about $100 billion from $300 billion, Bloomberg News reported on Wednesday, citing people familiar with the matter.

Last month, the Trump administration proposed a new, more expansive minerals deal, which gives Ukraine no future security guarantees but requires it to place in a joint investment fund all income from the exploitation of natural resources by state and private enterprises across Ukrainian territory.

The future agreement would require ratification in Ukraine's parliament and was expected to help economic growth in both countries, Svyrydenko said, but provided no more details.

"It will create opportunities for investment and development in Ukraine and establish conditions for tangible economic growth for both Ukraine and the United States," she said.

(Reporting by Yuliia Dysa and Olena Harmash; Editing by Frances Kerry, Ron Popeski and Bill Berkrot)